Structural  Designers 

Handbook 


w;  m 


LIBRARY 

OF   THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


STRUCTURAL  DESIGNERS' 
HANDBOOK 


GIVING  DIAGRAMS  AND   TABLES   FOR   THE   DESIGN   OF 
BEAMS,  GIRDERS  AND  COLUMNS  WITH  CALCU- 
LATIONS BASED  ON  THE  NEW  YORK 
CITY    BUILDING    CODE 


BY 

WILLIAM    FRY    SCOTT 

Structural  Engineer,   Member  American  Society  for  Testing  Materials 


or  THE 
UNIVERSITY 


NEW  YORK 

THE   ENGINEERING   NEWS   PUBLISHING   CO. 

1904 


Copyright,  1904 

Bt 
WILLIAM    FKY    SCOTT 


PREFACE* 

This  handbook,  essentially  a  diagrammatic  treatise  on  the  sub- 
ject of  Structural  Design,  contains  also  a  full  tabulation  of  the 
properties  of  market  shapes  of  materials. 

It  is  presented  to  the  architectural  and  engineering  professions 
with  the  thought  that  it  may  be  the  means  of  shortening  and  pos- 
sibly eliminating  much  of  the  computation  and  drudgery  which  are 
necessary  accompaniments  of  structural  designing. 

It  is  hoped  that  it  may  prove  useful  to  the  expert  designer, 
since  the  diagrams  presented  are  time-saving  devices ;  useful  and 
suggestive  to  the  non-expert  and  the  student,  since  the  diagrams 
illustrate  graphically  the  relations  of  the  various  factors  of  propor- 
tion, span  loading,  etc.,  for  the  variable  conditions  of  ordinary 
practice. 

Throughout  the  work  the  New  York  Building  Code  has  been 
followed,  because  it  is  everywhere  recognized  as  conservative  and 
safe. 

W.  F.  S. 

New  York,  July,  1904. 


894 


CONTENTS. 


PART  I.     SYNOPSIS  OF  MECHANICS  OF  THE 
BEAM  AND  COLUMN. 

'CHAPTER  I.     BEAMS. 

Page 

Span    ....................................................  1 

Cross   Section    ............................................  1 

Section  Moment   ..........................................  1 

Unit   Stress    ..............................................  2 

Manner  of  Support   .......................................  2 

Deflection   ...............................................  2 

End  Reactions   ...........................................  3 

Buckling  of  Compression  Flange  ...........................  4 

Loads  on  Beams    ..................  ;  ......................  4 

Conventional  Methods  of  Treating  Loads  on  Floor  Girders.  ...  5 

Conventional  Methods  of  Considering  Loads  on  Grillage  Beams  7 

CHAPTER  II.    COLUMNS. 

Concentric    Loads    ............................  .  ...........  8 

Eccentric  Loads   ..........................................  & 


PART  II.     BEAMWORK. 

CHAPTER  III.     FLOOR  FRAMING. 

Utility  of  Diagrams  .....................................      11 

Explanation   of  Diagrams   1   to  15    .......................      12 

Explanation  of  Tables   1  to  15  .............................  13 

Explanation  of  Diagrams  16  to  21  .........................      14 

Explanation  of  Diagram  22   ..............................      15 

Explanation  of  Tables  of  Properties  of  Shapes  .............      1(J 

Tables  1  to  15.  Giving  Percentage  of  Allowable  load,   Spac- 
ing and  End  Reaction  for  I-Beams  from  3-in.  x  5.5  Ib.  to 
24-in.   x  80-lb  .......................................  18-46 

Diagrams  1  to  15.     Giving  Allowable  Uniform  Load,   Spac- 
ing, Span,  etc.,  for  I-Beams  from  3-in.  1  x  5.5-lb.  to  24- 
in.  x  80-lb  .........................................  18-46 

Diagrams  16  to  21.     Giving  Allowable  Uniform  Load,  Spac- 
ing, Span,  etc.,  for  Angles  and  Tees  as  Beams  or  Gir- 
ders ...........................................  48-51 

Diagram  22.  For  Reducing  the  Value  of  a  Concentrated 
Load  to  an  Equivalent  Value  of  Uniform  Load  per 
Unit  Floor  Area  ...................................  52 

CHAPTER  IV.      SPANDREL  BEAMS. 

Explanation  of  Diagram  23  ..............................     53 

Explanation  of  Diagrams  24,  25,  26  .......................     54 

Diagram  23.  For  Giving  an  Equivalent  Value  of  Load  Con- 
centrated in  the  Middle  of  a  Span  for  any  Value  of  a 
Concentrated  Load  at  any  Other  Point  ................  56 


vi  CONTENTS, 

Diagram  24.     For  giving  the  Allowable  Load  on  Standard 

and  Special  3-in.  to  15-in.  I-Beams 57 

Diagram  25.      For  giving  the  Allowable  Load   on   Standard 

and  Special  10-in.   to  24-in.  I-Beams   58 

Diagram  26.     For  giving  the  Allowable  Load  on  3-in.  to  15- 

in.  Standard  and  Special  Channels 59 

CHAPTER  V.     GRILLAGE  BEAMS. 

Footings    60 

Design   60 

Bending   60 

Buckling  of  the  Web 62 

Explanation  of  Diagram  27 62 

Diagram  27.  For  giving  Size,  Weight  and  Spacing  of  I- 
Beams  necessary  for  each  of  the  several  tiers  in  a  gril- 
lage footing 63 

Example  of  Use  of  Diagram 63 

CHAPTER  VI.     END  REACTIONS. 

Explanation  of  Diagram  28 65 

Design  >and  'Sizes  of  Standard  Connection  Angles 66 

Explanation  of  Table  16 67 

Design  of  Bearing  Plates 68 

Explanation  of  Diagram  29 68 

Table  16.  For  giving  Maximum  Allowable  End  Reaction  on 

Standard  and  Special  Connection  Angles,  also  Relative 

Values  of  the  Several  Sizes  of  Rivets 69 

Diagnam  28.  For  giving  Values  for  Rivet  Requirements  in 

Connection  Angles,  also  Areas1  for  Bearing  Plates 70 

Diagram  29.  For  giving  Thickness  of  Beam  Plates  of  Cast 

Iron,  Wrought  Iron  or  Steel 71 

PART  III.     COLUMNS  AND  TRUSS  MEMBERS. 

CHAPTER   VII.      STEEL  COLUMNS. 

Ratio  of   Slenderness    73 

Explanation  of  Diagrams  30  to  34 73-78 

Diagram  30.  For  giving  the  Radius  of  Gyration  of  the  most 
Common  Forms  of  Column  Sections  of  Wood,  Cast  Iron 
or  Steel  79 

Diagram  31.  For  giving  the  Radius  of  Gyration  of  the  Most 

Common  Forms  of  Built-up  Column  Sections  80 

Diagram  32.  For  giving  the  Ratio  of  Slenderness  of  a  Col- 
umn    81 

Diagram  33.  For  giving  the  Safe  Loads  on  Steel  Columns  as 
Called  for  by  the  New  York  Building  Code  for  Ratios  of 
Slenderness  up  to  120  and  <as  Recommended  by  the  Au- 
thor for  Ratios  Between  120  and  200 82 

Diagram  34.  Eccentric  Loading  on  Columns.  For  giving 
Percentage  of  Material  Necessary  to  Add  to  the  Cross- 
Section  of  a  Column  for  'any  Eccentricity  of  the  Center 
of  Gravity  of  Its  Load,  with  Reference  to  the  Axial 
Planes  Through  Its  Neutral  Axis' 83 


CONTENTS.  vii 

Page 
CHAPTER  VIII.     TABLES. 

Explanation  of  Tables,  giving  Properties  of  Single  and  Built- 
up  Steel  Shapes  of  I-Beams,  Channels,  Angles,  Tees, 
Zees  and  Flats  for  Use  in  Columns,  Beams  and  Trusses  84 

Table  17.  Steel  I-Beams'.  For  Beams,  Girders,  Columns  or 

Truss  Members  90 

Table  18.  Steel  Channels  for  Beams,  Girders,  Columns  or 

Truss  Members  94 

Table  19.     Plate  and  Channel  Columns 95 

Table  20.  Steel  Angles  (even  legs)  for  Beams,  Girders,  Col- 
umns or  Truss  Members . 102 

Table  21.  Steel  Angles  (uneven  legs)  for  Beams,  Girders, 

Columns  or  Truss  Members 104 

Table  22.  Plate  and  Angle  Columns,  With  and  Without 

Cover  Plates  107 

Table  23.  Steel  Tees  for  Beams,  Girders,  Columns  or  Truss1 

Members  108 

Table  24.  Steel  Zee-bars  for  Beams,  Girders,  Columns  or 

Truss  Memtbers 110 

Table  25.     Weights  of  Flat  Rolled  Steel Ill 

CHAPTER  IX.     CAST-IRON  COLUMNS. 

Explanation  of  Diagrams  35,  36 113 

Diagram  35.  For  giving  the  Safe  Loads  on  Cast-iron  Col- 
umns' as  Specified  by  the  New  York  Building  Code. . .  .  114 

Diagram  36.  For  giving  the  Safe  Loads  on  Cast-iron  Col- 
umns as  Recommended  by  the  Author 115 

Tables  26  to  30.  Weight  and  Thickness  of  Metal  of  Cast-iron 

Column  Sections  116-118 

Table  31.  Weight  and  Thickness  of  Metal  of  Cast-iron  Gas 

Pipe  118 

PART  IV.     MISCELLANEOUS. 

CHAPTER  X.     LOADS. 

Explanation  of  Diagrams  37  and  38 119 

Diagram  37.  For  Giving  the  Weight  of  Steel  Required  in 

Floors  where  the  Loads  are  a  Minimum 120 

Diagram  38.  For  Giving  the  Weight  of  Steel  Required  in 

Floors  where  the  Loads  are  a  Maximum 121 

Diagram  39.  For  Giving  the  Weight  of  Joists  per  Square  Foot 

of  Floor 122 

Floor  Arches 123 

Flooring  Material 123 

Partitions  124 

Brick  Walls  124 

Live  Loads  on  Floors 125 

On  Footings 125 

Wind  Pressure  on  Buildings 125 

CHAPTER   XI.— UNIT    STRESSES. 

Safe  Load  on  Masonry  Work 12fi 

Strength   of   Columns .    126 


viii  CONTENTS. 

Page 

Working  Stresses 127 

Compression 127 

Tension   128 

Shear    128 

Safe  Extreme  Fiber  Stress 128 

Bearing  Capacity  of  Soil 128 

CHAPTER  XII.— BRICK  WALLS. 

Explanation   of   Diagram  40 129 

Diagram  40.  For  Giving  Thickness  and  Weight  of  Walls  for 
Skeleton  Structures,  Warehouses  or  Dwelling  Houses  Ac- 
cording to  the  New  York  Building  Code 132 

CHAPTER  XIII.— GERMAN,  BELGIAN  AND  ENGLISH 
I-BEAMS. 

Explanation  of  Tables  32,  33  and  34 133 

Table  32.  Properties  of  German  I-Beams 134 

Table  33.   Properties  of  Belgian   I-Beams 134 

Table  34.  Properties  of  English  I-Beams 134 

CHAPTER  XIV.— FLEXURAL  EFFICIENCY  OF  I-BEAMS 
AND  CHANNELS. 

Explanation   of   Diagram   41 136 

Diagram  41.     For  Giving  the  Relative  Flexural  Efficiency  of 

I-Beams  and  Channels  per  Pound  of  Steel 137 


CHAPTER   XV.— BASES   AND   LINTELS    OP  CAST  IRON. 

Methods  of  Design 138 

Explanation  of  Diagram  42 139 

Diagram  42,  For  Giving  the  Minimum  Thickness  for  Bottom 

Plate  of  Oast-iron  Shoes 140 

CHAPTER  XVI.— WOODEN  BEAMS  AND  POSTS. 

Explanation  of  Diagrams  43  to  51 142,  143 

Diagrams  43  and  44.  For  Giving  the  Safe  Load  on  White 
Pine,  Spruce  or  Chestnut  Joists  for  Each  Inch  in 
Breadth  144,  145 

Diagrams  45  and  46.  For  Giving  the  Safe  Load  on  Long  Leaf 
Yellow  Pine  or  Locust  Joists  for  Each  Inch  in  Breadth 

146,  147 

Diagrams  47  and  48.  For  Giving  the  Safe  Load  on  White 
Pine,  Spruce  or  Chestnut  Girders  for  Each  Inch  in 
Breadth 148,  149 

Diagrams  49  and  50.  For  Giving  the  Safe  Load  on  Long  Leaf 
Yellow  Pine  or  Locust  Girders  for  Each  Inch  in  Breadth. 

150,  151 

Diagram  51.  For  Giving  Safe  Load  on  White  Pine,  White 
Oak  and  Yellow  Pine  Posts,  Ratio  of  Length  to  Least 
Radius  of  Gyration,  Area  of  Section  in  Square  Inches  and 
Ratio  of  Length  to  Least  Diameter  (both  in  inches) ....  152 


DESIGNERS'  HANDBOOK. 


Part  L     Synopsis  of  Mechanics  of  the  Beam  and  Column* 

CHAPTER  L— BEAMS. 

The  resistance  of  a  beam  to  bending  is  the  main  item  that  de- 
termines its  strength,  so  much  so,  in  fact,  that  the  other  deter- 
minative factors  are  often  forgotten  or  at  least  not  given  due  at- 
tention. The  resistance  to  bending  depends  upon  the  span  of  the 
beam,  its  cross  section,  the  unit  stress  permissible  in  the  material, 
and  the  manner  of  support  of  the  beam. 

The  SPAN  of  a  beam  where  the  latter  is  simply  supported,  is 
measured  between  centers  of  members  by  which  the  beam  is  sup- 
ported in  case  of  end  framing  connections,  or,  in  case  the  beam 
rests  upon  a  wall  or  other  support,  between  centers  of  bearing 
plates. 

The  CROSS  SECTION  of  the  beam  affects  its  strength  in  a 
manner  depending  upon  the  moment  of  inertia  and  the  depth  of 
the  cross  section,  both  measured  from  the  neutral  axis.  For  any 
given  cross  section  these  quantities  are  constant,  and  hence  do 
not  enter  into  the  diagrams  presented  in  this  book  since  each 
standard  shape  is  represented  by  a  separate  diagram,  or,  in  the 
case  of  spandrel  or  grillage  beams,  each  shape  is  represented  by 
a  line  on  the  diagram. 

For  cases  where  calculations  of  beams  are  made  without 
using  diagrams,  the  tables  given  in  Chapter  VIII  give  the  SECTION- 
MOMENT  (symbol  Ma )  for  each  structural  steel  shape.  The  sec- 
tion-moment* is  a  quantity  obtained  by  multiplying  the  maximum 
allowable  fiber  stress  by  the  moment  of  inertia  of  the  cross  section, 
and  dividing  by  the  distance  of  the  extreme  fiber  from  the  neutral 
axis.  It  will  be  recognized  to  be  the  resisting  property  that  op- 
poses the  bending  moment  (symbol  Mb)  of  the  external  forces. 

*The  author  has  taken  the  liberty  to  coin  this  word,  because  of  the 
confusion  of  terms  in  reference  to  this  property  of  a  beam.  Also,  because 
there  is  as  much  distinction  between  the  section-moment  and  the  external 
bending  moment  as  between  the  fiber  stress  and  the  external  load  produc- 
ing it. 

(1) 


2  STRUCTURAL    DESIGNERS'    HANDBOOK. 

By  computing  the  maximum  bending  moment  due  to  the  ex- 
ternal forces,  and  referring  to  the  values  of  section-moments,  given 
in  the  aforementioned  tables,  the  proper  structural  shape  to  be 
used  can  readily  be  found.  (It  should  be  noted  that  the  section- 
moments  are  given  in  foot-pounds  for  angles  and  tees  but  in  foot- 
tons  for  all  other  shapes.) 

The  maximum  UNIT  STEESS  permissible  in  structural  steel 
beams  is  throughout  this  book  taken  at  16,000  Ibs.  per  sq.  in. 
This  is  in  accordance  with  the  provisions  of  the  "Code"  (N.  Y.  C), 
with  the  tables  contained  in  the  pocket  books  of  the  steel  manu- 
facturers, and  with  nearly  all  specifications  for  beamwork  in  build- 
ings. 

The  MANNER  OF  SUPPORT  of  the  beam  affects  its  strength 
quite  materially.  By  far  the  most  common  case  is  where  the 
ends  are  "simply  supported."  The  diagrams,  with  the  single  excep- 
tion of  that  for  grillage  beams, *  are  based  exclusively  upon  this 
case,  and  for  convenience  in  calculating  the  strength  of  beams  under 
other  conditions  of  support,  the  following  formulas  are  given: 

WL  =  Ms,  for  a  cantilever  beam  with  load  concentrated  at  the  end.     (i) 
"     =»    2  Ms,  for  a  cantilever  beam   with  load  uniformly  distributed.     (2) 
'    =    4  Ms,  for  a  simple  beam  supported  at  the  ends,  and  load  con- 
centrated in  the  middle.  (3) 
"    =    8  Ms,  for  a  simple  beam  supported  at  the  ends,  and  load  uni- 
formly distributed.  (4) 
"    =  5.2  Ms,  for  a  beam  with  one  end  fixed  and  the  other  end  sup- 
ported, and  load  concentrated  near  the  middle.             (5) 
"    =    8  Ms,  for  a  beam  with  both  ends  fixed,  and  load  concentrated 

in  the   middle.  (6) 

"    =  12  Ms,  for  a  beam  with  both  ends  fixed,  and  load  uniformly  dis- 
tributed. C?) 
where 

W.  =  Total  load  on  beam,  in  tons  or  pounds. 
L.    =  Span  of  beam,  in  feet. 
Ms.  =  Section-moment,  in  foot-tons  or  foot-pounds. 

The  question  of  the  DEFLECTION  of  beams  is  one  of  special 
importance  in  many  cases,  as  for  instance,  where  plastered  ceil- 
ings are  involved.  One  four-hundredth  of  the  span  should  gen- 
erally be  the  limit  for  such  cases.  The  diagrams  for  spandrel  and 
floor  beams  are  calculated  for  a  limiting  deflection  of  this  amount. 
For  general  practice  there  should  be  no  objection  to  this  limit, 


*These  are  virtually  cases  of  cantilever  beams. 


BEAMS.  3 

even  where  plastered  ceilings  are  not  involved.  For  bridge  work 
and  some  other  cases,  the  deflection  of  beams  is  not  usually  con- 
sidered, in  which  case  the  diagrams  may  be  used  by  placing  a 
straight  edge  on  the  left  hand  portion  of  the  curve  and  determining 
the  intersection  of  this  portion  produced  for  the  span  and  spacing 
required. 

For  convenience  in  calculating  the  strength  of  beams  for  a 
limiting  deflection  of  one  four-hundredth  of  the  span,  under  the 
several  more  common  conditions  of  support,  the  following 
formulas  are  given : 

W  L2  =   0.566  h  Ms,  for  a  cantilever  beam  with  load  concentrated  at 

the  end.  (8) 

"     =1.51     h  Ms,  for  a  cantilever  beam  with  load  uniformly  dis- 
tributed. (9) 
"     =   9-°5     h   Ms,  for  a  simple  beam  supported  at  the  ends,  and 

load  concentrated  in  the  middle.  (10) 

"     =  14.5      h  Ms,  for  a  simple  beam  supported  at  the  ends,  and  load 

uniformly  distributed.  (n) 

"  =  10.35  h  Ms,  for  a  beam  with  one  end  fixed,  and  the  other  end 
supported,  and  load  concentrated,  near  the 
middle.  (12) 

=  35.2      h  Ms,  for  a  beam  with  both  ends  fixed,  and  load  con- 
centrated in  the  middle.  (13) 
•     "      =  72.5       h  Ms,  for  a  beam  with  both  ends  fixed,  and  load  uni- 
formly distributed.                                                        (14) 
where 

W  =  Total  load  on  beam,  in  tons. 
L   =  Span  of  beam,  in  feet. 

h    =  Depth  of  beam,  in  inches  (for  symmetrical  sections  only). 
Ms  =  Section-moment,  in  foot-tons. 

The  upward  reaction  of  the  support  against  the  beam,  is  an 
important  matter  as  affecting  its  strength,  and  it  should  be  kept  in 
mind  in  every  case  of  their  design. 

THE  END  REACTIONS  due  to  uniformly  loading  standard 
beams  up  to  their  full  allowable  flexure  strength  for  various  spans 
are  given  on  Diagram  No.  28  in  Chapter  VI.  These  are  the  ex- 
ternal loads  which  are  resisted  by  stresses  in  the  webs  of  the 
beams.  These  stresses  are  of  importance  principally  in  very  short 
beams  loaded  to  their  full  bending  capacity.  The  following  is  a 
discussion  on  these  stresses,  all  mathematical  reasoning  being- 
omitted  for  the  sake  of  brevity  : 

The  end  reaction,  divided  by  the  area  of  the  web  (usually  considering 
the  height  of  the  beam  times  the  web  thickness),  equals  the  unit  intensity 


4  STRUCTURAL    DESIGNERS'    HANDBOOK'. 

of  the  vertical  shearing  stress  in  the  web.  While  not  absolutely  correct, 
the  above  statement  is  practically  true.  This  unit  intensity  of  vertical  shear 
is  equal  to  the  unit  intensity  of  shearing  stress  acting  at  angles  of  45°  with 
the  neutral  axis  of  the  beam,  and  these  again  are  equivalent  to  direct  com- 
pressive  and  tensile  stresses  in  the  web,  acting  at  right  angles  to  each  other. 
The  compressive  stress  will  evidently  tend  to  buckle  the  web,  while  the 
tensile  stress  will  tend  to  hold  it  in  its  true  plane.  Neglecting  the  value  of 
the  tensile  stress  (which  is  really  indeterminate),  or  in  other  words,  placing 
the  "factor  of  ignorance"  on  the  safe  side  of  the  problem,  then  the  unit 
intensity  of  the  compressive  stress  should  for  safety  not  exceed  the  allowable 
unit  compressive  stress  in  any  strip  of  the  web  between  the  fillets,  at  45° 
with  the  neutral  axis  of  the  beam. 

When  the  ratio  of  the  length  of  any  such  strip  to  the  least  radius  of 
gyration  of  the  web  exceeds  no  (which  is  the  point  at  which  the  shearing 
strength  practically  becomes  equal  to  the  compressive  strength)  then  the 
allowable  end  reaction  should  be  determined  by  the  permissible  compressive 
stress  in  the  web;  when  the  ratio  is  less  than  no  the  allowable  reaction 
should  be  determined  by  the  permissible  shearing  stress.  -  . 

Tables  opposite  each  of  the  Diagrams  Nos.  I  to  15  and  also 
the  tables  for  I-beams  and  channels  in  Chapter  VIII  give  these 
values,  according  to  the  "Code"  (N.  Y.  C.)  requirements  for  shear- 
ing and  compressive  stresses.  (See  Chap.  XI  on  unit  stresses.) 

BUCKLING  OF  COMPRESSION  FLANGE.— Floor  beams  usu- 
ally have  their  compression  flanges  supported  laterally  by  the  floor, 
arches,  and  the  girders  have  their  flanges  supported  by  the  beams 
which  frame  into  them.  When  the  lateral  supports  are  so  far  apart 
that  the  upper  flange  of  the  beam,  considered  as  a  column,  would 
begin  to  deflect  under  a  load  equivalent  to  the  compressive  stress 
in  that  flange,  then  the  load  on  the  beam  in  flexure  should  be  re- 
duced. In  the  Diagrams  Nos.  I  to  15,  this  reduction  of  load  is 
given  for  different  lengths  of  flange  between  lateral  supports.  As 
is  explained  in  Chapter  III,  a  scale  at  the  bottom  of  these  dia- 
grams gives  for  any  unsupported  length  of  flange  in  feet  the  maxi- 
mum percentage  of  full  load  that  can  be  safely  carried  without 
danger  of  buckling  of  the  upper  flange. 

LOADS  ON  BEAMS. — The  bending  stress  due  to  a  concentrated 
load  depends  upon  the  amount  of  the  load  and  its  position  on  the 
beam  with  reference  to  the  span.  The  most  unfavorable  position 
is  at  the  center,  the  bending  stress  in  this  case  being  twice  that  due 
to  the  same  load  uniformly  distributed.  As  the  load  moves  towards 
either  end,  the  bending  stress  produced  by  it  decreases.  In  each 
case,  the  greatest  stress  in  the  beam  is  directly  below  the  load. 


BEAMS.  5 

Thus,  when  the  load  is  not  at  the  center  of  the  beam,  the  stress  at 
the  center  due  to  the  load  is  less  than  the  stress  directly  under  the 
load. 

This  is  of  importance  in  the  case  of  combined  loads.  The 
bending  stress  due  to  a  combination  of  concentrated  loads  (with 
or  without  a  uniform  load)  is  greatest  at  a  point  of  the  beam 
near  the  center  of  gravity  of  the  loads.  Moreover,  the  maximum 
stress  is  somewhat  less  than  the  sum  of  the  maximum  stresses  due 
to  each  of  the  uniform  or  concentrated  loads  acting  alone. 


CONVENTIONAL  METHODS  OF  CONSIDERING  LOADS 

ON    BEAMS. 

The  scope  of  the  present  book  will  not  admit  of  discussing 
more  than  the  two  special  cases,  under  this  heading,  that  are  in- 
volved in  the  methods  of  constructing  the  diagrams  on  beamwork. 
The  first  is  a  consideration  of  the  conventional  treatment  of  uni- 
form loading  on  floor  girders  in  terms  of  unit  floor  area.  The 
second  is  a  discussion  of  the  two  principal  conventional  methods 
of  considering  the  loads  on  grillage  beams. 

CONVENTIONAL  METHOD  OF  TREATING  LOADS  ON  FLOOR 
GIRDERS. — The  diagrams  in  Chapter  III  on  beams  refer  directly  to- 
uniform  loading  per  square  foot  of  floor.  Since  the  main  girders  in 
a  floor  support  the  floor  beams,  and  thus  carry  what  are  essentially 
concentrated  loads,  it  may  at  first  sight  be  thought  that  the  same 
diagrams  could  not  be  directly  applicable  to  girders.  This  is  not  the 
case,  however,  as  will  be  evident  by  considering  a  girder  with  a  single 
concentrated  load  in  the  center.  The  strength  of  this  girder  is  or- 
dinarily found  in  terms  of  the  load  and  the  span  of  the  girder.  The 
external  bending  moment,  for  instance,  is  equal  to  one-fourth  of 
the  span  in  feet  multiplied  by  the  amount  of  the  concentrated  load 
in  tons  or  pounds,  according  to  the  units  adopted  by  the  designer. 
Suppose,  now,  that  this  concentrated  load  is  clue  to  two  beams 
framing  into  the  girder,  one  on  each  side,  and  in  order  to  simplify 
the  problem,  suppose  the  spans  of  these  two  beams  to  be  equal,  of 
the  value  B.*  Then  if  L  equals  the  span  of  the  girder,  W  the  load- 


*If   the   beams   framing  into   the   girder   have   spans   that   are   unequal,, 
then  (B)  is  equal  to  one-half  the  sum  of  the  spans. 


6  STRUCTURAL    DESIGNERS'    HANDBOOK. 

ing  on  the  beams  in  pounds  per  square  foot  of  floor,  Mb  the  exter- 
nal bending  moment  on  the  girder,  and  C  the  concentrated  load  on 
the  girder  due  to  the  two  beams,  we  have, 

L  C  WBL 

Mb  = ,  and  C  = , 


or 

WBL2 
Mb  =  


8 

But  if  the  girder  were  considered  loaded  with  a  uniform  load 
W  per  square  foot,  distributed  over  the  area  represented  by  breadth 
B  and  length  L,  the  moment  on  the  girder  would  be 

WBL2 

Mb  ==  , 

8 

which  is  the  same  as  found  by  the  other  method. 

It  will  be  found  on  analysis,  that  the  result  obtained  in  this 
particular  case  can  be  safely  applied  to  the  case  of  a  girder  with 
any  number  of  beams  framing  into  it.  Thus,  so  long  as  girders 
are  designed  in  terms  of  the  actual  area  enclosed  within  the 
parallelogram  having  a  breadth  B  and  length  L,  and  the  uniform 
load  W  per  unit  area,  the  diagrams  will  be  found  to  give  safe  re- 
sults. In  all  cases  where  odd  numbers  of  beams  (even  number  of 
spaces  between  ends)  frame  into  girders,  the  values  given  in  the 
diagrams  are  just  as  true  for  girders  as  for  simple  beams,  pro- 
vided the  sum  of  the  spans  of  the  floor  arches  does  not  exceed 
length  L,  while  in  the  case  of  even  numbers  of  beams  framing  into 
girders,  the  diagrams  give  values  that  are  a  little  safer  than  in  the 
other  cases.  There  are  only  three  cases  where  the  difference  is 
perceptible — where  two,  four  or  six  beams  frame  into  the  girder 
(respectively  three,  five  or  seven  spaces  between  the  ends  of  the 
girder).  They  differ  from  the  diagram  values  as  follows  : 

Two   beams,  Mb  =  %  W  B  L2  =  o.m  WBL* 

Four  beams,  Mb  =  %o  W  B  L2  =  0.120  W  B  LJ 

Six  beams,  Mb  =  V«  W  B  L2  =  0.122  W  B  L1 

Uniform  load,  Mb  =  Va  W  B  L2  =  0.125  WBL2 

For  more  than  six  beams,  the  moment  practically  equals  that 
for  uniform  load.  For  the  three  cases  given  above,  the  permissible 
loading  on  the  girder  is  respectively  \2.\%,  4%  and  2%  greater 


BEAMS.  7 

than  that  given  by  the  diagrams.  Therefore  in  these  three  cases 
the  results  obtained  from  the  diagrams  can  be  corrected  as  follows : 

Increase  the  load  per  square  foot  by  12%%,  4%  and  2%  re- 
spectively, for  the  three  cases  ;  or  increase  the  spacing  of  the  girders 
by  the  same  percentages,  in  which  case  the  load  is  not  changed ;  or 
increase  the  span  of  the  girders  6%,  2%  and  i%  respectively. 

CONVENTIONAL  METHODS  OF  CONSIDERING  LOADS  ON 
GRILLAGE  BEAMS. — Correctly  speaking  there  is  only  one  condi- 
tion that  actually  represents  the  effect  of  the  load  on  a  grillage  foot- 
ing, but  usage  in  design  is  sometimes  contradictory  when  the  prem- 
ises are  not  well  understood.  This  is  well  illustrated  in  two  meth- 
ods of  designing  grillage  beams  in  footings.  For  instance,  one 
method  considers  the  active  portion  of  the  load  to  be  on  the  pro- 
jecting length  of  the  beam  only,  and  the  bending  moment  calcu- 
lated at  the  edge  of  the  base  above,  or  the  edge  of  the  tier  of  beams, 
if  such  exists,  is  assumed  to  be  the  maximum  bending  moment  on 
the  footing.  The  second  method  considers  the  bending  moment 
at  the  center,  due  to  all  the  external  forces  acting  on  the  footing. 

The  formulas  for  the  two  methods  are: 

First  Method: 

Waa 
Mb= (15) 

2 

where     Mb  =  Bending  moment  under  edge  of  tier  above, 
W  =  Load  per  unit  length  of  beam, 
a  =  Length  of  projecting  portion  of  beam. 
Second  Method: 


a      r          b  ]       W  a2      f            b    ") 
=  W  —     |    a  +  —   » i+ 

2  2    J  2  I  2a     J 


(16) 


where     Mb  =  Maximum  bending  moment  at  center, 
b  =  Width  of  base  or  tier  above, 
a  =  Projecting  portion  of  beam. 

Comparing  these  two  formulas,  the  maximum  bending  rno- 
b 

ment  on  the  footing  is  I  + times  the  bending  moment  occur- 

2a 
ring  under  the  edge  of  the  tier  above. 

It  will  thus  be  seen  that  the  bending  moment  at  the  center  is 
b 

greater  by  the  percentage than  the  moment  at  the  edge  of  the 

2a 
base.    The  use  of  formula  (15)  would  therefore  appear  to  lead  to 


8  STRUCTURAL    DESIGNERS'    HANDBOOK. 

an  unsafe  design.  It  has  been  found  by  experience,  however, 
that  the  concrete  in  the  footing  goes  to  form  a  composite  beam  of 
considerable  excess  strength  over  that  of  the  steel  beams  alone,  and 
designs  have  been  made  by  experienced  engineers  in  which  this 
excess  has  apparently  been  assumed  to  be  from  25%  to  75%  (on 
the  basis  of  16,000  Ibs.  per  sq.  in.  maximum  fiber  stress). 

This  question  will  be  further  discussed  in  the  Chapter  on  Grill- 
age Beams. 


CHAPTER  II.— COLUMNS. 

A  column  is  designed  to  resist  forces  which  usually  act  in  the 
direction  of  its  axis — the  center  of  gravity  of  these  forces  may 
coincide  with  or  may  be  a  short  distance  from  and  parallel  to  this 
axis.  In  the  former  case  they  are  called  "Concentric"  loads,  in 
the  latter  case  "Eccentric"  loads. 

CONCENTRIC  LOADS.— A  column  in  direct  compression,  if 
secured  against  lateral  deflection  might  safely  be  designed  to  de- 
velop the  full  allowable  unit  compressive  stress  for  the  material. 
However,  if  any  slight  deflection  of  the  axis  from  a  straight  line 
takes  place,  the  load  acts  to  produce  flexure  stresses  in  addition  to 
the  direct  compressive  stress.  For  this  reason  columns  cannot 
safely  be  designed  for  the  full  working  unit  stress  that  is  allowed  for 
the  material  in  simple  compression.  This  tendency  of  a  column  to 
deflect  depends  upon  the  ratio  between  its  length  and  least  radius  of 
gyration.  This  ratio  may  be  called  the  ratio  of  slcndcrness  of  the 
column.  Column  formulas  based  on  this  ratio  exist  in  great  variety 
— the  "load"  diagrams  for  columns  (in  Part  III)  are  based  on  the 
formulas  prescribed  by  the  "Code"  (N.  Y.  C.). 

ECCENTRIC  LOADS. — When  a  column  is  eccentrically  loaded 
the  stresses  produced  in  any  cross  section  are  a  uniform  com- 
pressive stress  of  the  same  value  as  would  be  produced  by  a  con- 
centric load  of  the  same  amount,  and  the  stresses  due  to  a  bending 
moment  caused  by  the  eccentricity  of  the  load.  The  sum  of  these 
stresses  is  a  maximum  on  the  compressive  side  of  a  cross  section  at 
or  near  the  bottom  of  the  bracket  which  transmits  the  larger  share 
of  the  eccentric  load  into  the  column,  and  it  is  a  minimum  at  the 
foot  of  the  column.  However,  as  the  cross  section  of  a  column  is 
usually  made  uniform  throughout  its-  length,  it  is  not  necessary  to 


COLUMNS. 


consider  any  but  the  maximum  stresses.  This  cross  section  is 
therefore  designed  so  that  the  sum  of  the  compressive  stresses  due 
to  the  bending  moment  and  the  compressive  stress  due  to  a  con- 
centric load  of  the  same  amount  shall  not  exceed  the  safe  unit  com- 
pressive stress  allowable  on  a  column  with  the  given  ratio  of  slen- 
derness. 

The  area  of  the  cross  section  of  a  column  required  to  resist 
the  compressive  stress  due  to  a  concentric  load  is  found  by  divid- 
ing the  load  by  the  allowable  unit  stress  obtained  from  the  afore- 
mentioned column  formulas,  while  the  area  required  to  resist  the 
compressive  stresses  due  to  the  eccentric  load  is  a  much  more  com- 
plex problem.  It  is  usually  based  on  the  following  considerations : 
Fig.  i  shows  a  column  eccentrically  loaded.  The  load  Pe  is  applied 
at  a  distance  a  from  the  neutral  axis  of  the  column  and  the  extreme 
fiber  of  the  column  is  at  a  distance  y  from  its  neutral  axis.  Then 
the  bending  moment  produced  in  the  column  by  the  eccentricity  of 
loading  is  expressed  by  the  formula. 

Mb  =  zP  (17) 

where  P  —  Pe  +  PC  and  z  equals  distance  from  the  neutral 
axis  to  the  center  of  gravity  of  the  loads;  and  the  required 
section-moment  is 

SI        S  A  r2 
MS  = — ,  (18) 

y  y 

in  which  S  represents  the  allowable  unit  stress  in  the 
material,  I  the  moment  of  inertia  of  the  cross  section  (I 
being  equal  to  the  area  A  of  the  section,  times  the  square 
of  r,  the  radius  of  gyration). 

Now  putting  the  section-moment  equal  to  the  external 
bending  moment, 

S  Ar2 
z  P  = , 


Pe 


\ 


ti\ 


-  y 


from   which 


Fig.  1. 


A=— 


zy 


(19) 


bending 


This  expression  shows  that  the  area    required    for 
alone  is  given  by  considering  the  eccentric  load  as  a  pure  concen- 
tric load,  and  multiplying  the  area  —  thus  considered,  by  a  factor 

S 
zy 

which  depends  upon  the  distance  of  the  center  of  gravity  of  the 


10  STRUCTURAL    DESIGNERS'    HANDBOOK'. 

loads  from  the  neutral  axis,  the  distance  of  the  extreme  fiber  from 
the  neutral  axis,  and  the  radius  of  gyration  of  the  section.  The 
term  z  y  is  conveniently  called  the  coefficient  of  eccentricity. 

z  y 

The  factor ,  it  should  be  noted,  simply  gives  the  percentage  of  area 

r 

of  a  column  section  as  calculated  for  a  concentric  load  which  it  is  necessary 
to  add  to  take  care  of  the  added  stress  due  to  the  eccentricity  of  the  load. 
If  the  load  is  eccentric  on  both  axes,  then  two  of  these  percentages  must 
be  determined.  Thus  the  area  of  a  column  which  is  eccentrically  loaded  in 
both  principal  directions  is  expressed  by  the  formula: 

z'  y'         z"  y'' 


Where  P  =  Pe  +  PC  =  total  load  on  the  column. 

S  =  allowable  unit  stress  in  the  material  and  determined  by  the 

minimum  radius  of  gyration. 

Z',  y'  and  r'  being  taken  about  the  minor  axis  and  z",  y"  and  r" 
about  the  major  axis. 

This  subject  will  be  continued  in  Chapter  VII    on  steel  col- 
umns. 


Part  IL — Beamwork. 

CHAPTER  III.— FLOOR  FRAMING. 

UTILITY  OF  DIAGRAMS.— The  strength  of  beams  and  girders* 
is  given  in  almost  all  books  on  the  subject  in  terms  of  the  total 
uniform  load  which  they  will  safely  carry.  If  the  beams  are  used 
in  floors,  where  the  loads  are  mostly  uniform  and  known  in  terms 
of  the  unit  floor  area,  it  is  necessary  to  perform  a  more  or  less 
lengthy  calculation  to  determine  the  spacing  of  the  floor  beams  un- 
der consideration,  and  these  calculations  have  to  be  repeated  for 
every  problem.  The  diagrams  in  this  chapter  eliminate  the  need 
for  calculations  of  this  sort,  and  enable  the  proper  spacing  of  beams 
and  girders  of  an  assumed  size  to  be  read  off  at  once  for  any  given 
span,  and  any  given  load  per  square  foot  of  floor. 

An  equally  important  application  of  the  diagrams  may  be 
made  at  an  earlier  stage  of  the  work.  It  is  quite  generally  recog- 
nized that  the  time  to  consider  economy  of  material  in  the  frame- 
work of  a  building  is  at  that  stage  of  the  development  of  the  plan 
when  the  architect  and  the  owner  are  "getting  together"  on  the 
matter  of  what  can  be  done  for  the  money  to  be  invested.  Any 
excess  in  the  span  of  beams  and  girders  over  the  minimum  re- 
quired by  the  particular  conditions  governing  in  each  case,  adds  to 
the  cost  of  the  steelwork.  The  diagrams  in  this  chapter  will  be 
found  useful  in  deciding  upon  an  economical  arrangement  of  col- 
umns in  such  cases.  It  will  be  evident  that  when  once  the  spacing 
of  columns  is  fixed,  there  can  be  comparatively  little  room  for  con- 
sideration of  economy  in  beam  arrangement. 

Thus  these  diagrams  will  be  found  valuable  in  preliminary 
work  for  two  special  reasons :  (i)  Several  possible  arrangements  of 
beams  and  girders  can  be  studied  in  a  few  minutes  by  their  use.  (2) 
The  weight  of  steel  for  every  case  being  given,  the  most  economical 

*The  word  "beam"  is  used  throughout  this  book  to  signify  beams  used 
as  joists  or  rafters,  and  the  word  "girder"  to  signify  beams  used  as  sup- 
ports for  joists  or  rafters. 

(ID 


12  STRUCTURAL    DESIGNERS'    HANDBOOK. 

arrangement  of  beams   and  girders   will  be   evident  without   any 
figuring. 

The  first  fifteen  diagrams  cover  the  standard  weight  of  I-beam 
in  each  of  the  various  sizes,  and  their  use  is  extended  to  channels 
and  special  I-beams  by  means  of  the  supplementary  tables  which 
are  placed  opposite  each  diagram.  The  next  six  diagrams  cover 
angles  and  tees  used  as  beams.  A  special  diagram  is  added  to  this 
group,  which  extends  its  use  to  the  consideration  of  minor  concen- 
trated loads  by  giving  an  equivalent  uniform  load. 

DIAGRAMS  FOR  I-BEAMS  AND  CHANNELS  (NOS.  1  TO  15):— 
A  separate  diagram  has  been  drawn  for  each  standard  I-beam; 
thus  Diagram  No.  6  refers  to  an  8-in.  beam.  Each  diagram  gives 
span,  spacing,  and  load  as  three  variables,  any  two  of  which  de- 
termine the  third  for  that  particular  section  of  beam.  The  abscissas 
represent  spans,  and  the  ordinates,  the  spacings  (distance  apart)  of 
beams.  Diagonal  lines  on  the  diagrams  represent  loads  per  square 
foot  of  floor. 

It  will  be  seen  on  inspecting  the  diagrams  that  the  right  hand  portion 
of  the  "load"  lines  makes  a  smaller  angle  with  the  vertical  than  the  left 
hand  portion  of  the  lines.  This  is  due  to  the  fact  that  above  a  certain 
length  of  span  the  deflection  becomes  the  limiting  factor  in  determining 
load  or  spacing.  To  the  left  of  the  bend  point  the  maximum  fiber  stress 
is  the  limiting  factor.  Thus  the  diagrams  always  insure  that  the  deflection 
will  not  exceed  one  four-hundredth  of  the  span.  In  case  it  is  desired  to 
neglect  the  question  of  deflection,  the  left  hand  portion  of  the  lines  may 
evidently  be  prolonged,  for  instance,  by  means  of  a  straight  edge  to  the 
desired  span. 

The  method  of  using  the  diagrams  is  quite  simple.  Suppose 
in  a  given  floor  plan  it  is  desired  to  use  a  certain  size  of  beam.  On 
the  diagram  for  this  size  of  beam  take  an  abscissa  equal  to  the  span 
and  follow  up  to  the  diagonal  line  representing  the  loading  per 
square  foot  of  floor.  The  horizontal  line  indicates  the  proper  spac- 
ing of  the  beams. 

On  the  right  hand  edge  of  each  diagram  will  be  found  a  scale 
of  weights  in  pounds.  This  scale  represents  the  weight  of  the  beams 
per  square  foot  of  floor.  Thus,  having  found  the  proper  spacing  as 
above,  the  same  horizontal  line  is  followed  to  the  right,  and  on  the 
scale  of  weights  will  be  found  the  corresponding  equivalent  weight 
of  the  beams  per  square  foot  of  floor. 

One  other  scale  will  be  found  on  the  diagrams,  at  the  lower 
edge,  just  above  the  scale  of  spans.  Here  is  given  for  dif- 


FLOOR    FRAMING.  13 

ferent  abscissas  a  series  of  percentages.  They  represent  the 
maximum  percentage  of  full  "bending"  load  that  is  allow- 
able consistent  with  safety  against  buckling  of  the  upper  flange  of  the 
beam.  The  abscissas  to  be  used  in  referring  to  this  scale  are  the 
unsupported  length  of  flange,  not  the  span  of  the  beam.  The  use  of 
this  scale  will  be  clear  from  what  has  been  said  in  Chapter  I  on  the 
subject  of  "Buckling  of  Compression  Flange." 

Then,  to  summarize,  each  of  the  diagrams  gives  :* 

(a)  The  allowable   uniformly  distributed  live  and  dead  load  on  floor 
beams  and  girders,   in   pounds  per  square  foot  of  floor,   for  any  span  or 
spacing  in  feet. 

(b)  The  allowable  spacing  center  to  center  of  floor  beams  or  girders, 
in    feet   or    fractions    thereof,    for    any    span    and   any   uniform   loading   in 
pounds  per  square  foot  of  floor. 

(c)  The  allowable   span   in   feet   for   floor   beams   or   girders,   for   any 
uniform  loading  and  any  spacing. 

(d)  The  weight  of  steel  in  any  of  these  floor  beams  or  girders  in  pounds 
per  square  foot  of  floor. 

(e)  The  percentage  of  load  allowable  on  a  single  beam  or  girder  for 
any  unsupported  length  of  top  flange  in  feet. 

SUPPLEMENTARY  TABLES  (NOS.  1  TO  15) :— In  connection 
with  each  diagram,  just  referred  to,  is  given  a  table  which  greatly 
extends  its  use.  The  diagram,  it  will  be  remembered,  gives  values 
for  the  "standard"  weight  of  I-beam.  The  table  facing  the  diagram 
gives  a  set  of  factors  for  the  "special"  weights  of  I-beam  of  the 
same  depth,  and  for  all  the  "standard"  and  "special"  weights  of 
channel  of  the  same  depth ;  also,  for  zees  and  bulb  angles  of  corre- 
sponding depth.  By  the  use  of  these  factors,  which  are  expressed 
in  per  cent,  of  the  diagram  values,  the  results  obtained  from  the 
diagram  are  directly  applicable  to  all  the  other  weights  and  sections 
given  in  the  supplementary  table. 

For  instance,  when  a  value  of  load  or  spacing  has  been  found  from 
the  diagram  for  a  5-in.  I-beam,  weighing  9.75  Ibs.  per  ft.,  and  it  is  desired 
to  use  instead  a  5-in  channel,  weighing  6.5  Ibs.  per  ft.,  the  percentage 
factor  63  is  read  from  the  supplementary  table,  and  the  load  or  spacing 
found,  when  multiplied  by  0.63  gives  the  correct  load  or  spacing  for  the 
channel. 

A  further  column  in  the  tables  gives  the  maximum  end  reactions 
allowable  to  avoid  buckling  or  shearing  in  the  web  of  the  beam  over 
the  supports.  For  short  beams  it  is  always  essential  to  see  that  the 
load  permitted  on  the  beam  for  bending  does  not  give  a  greater  end 

*On  a  basis  of  a  maximum  stress  of  16,000  Ibs.  per  sq.  in. 


14  STRUCTURAL    DESIGNERS'    HANDBOOK'. 

reaction*  than  that  shown  in  the  table.  It  the  actual  reaction  ex- 
ceeds the  tabular  value,  then  the  load  should  be  reduced,  or  another 
beam  should  be  used,  or  stiffener  angles  should  be  riveted  to  the 
web. 

It  will  be  observed  that  the  supplementary  tables  give  parallel  sets 
of  values,  headed  respectively,  "Carnegie,  Cambria,  Jones  &  Laughlins, 
Phoenix;"  "Pencoyd"  and  "Passaic." 

The  reason  for  this  is  the  following:  The  standard  sections  of  steel 
beams,  channels  and  angles  adopted  by  the  American  Association  of  Steel 
Manufacturers  in  1896  are  now  adopted  by  nearly  all  the  rolling  mills  in- 
this  country.  There  are  some  exceptions,  however,  that  are  typical;  there- 
fore the  tables  have  been  compiled  with  a  view  of  making  this  hand-book 
a  compendium  of  the  market  shapes  used  in  structural  work.  The  values 
for  percentages  and  end  reactions  were,  however,  computed  by  the  author. 
No  attempt  is  made  to  give  a  list  of  rolling  mills.  Neither  was  there  an 
inclination  to  discriminate  in  favor  of  the  mills  mentioned  in  the  classifica- 
tion. The  principle  adopted  in  making  up  these  tables,  was  to  take  the 
Manufacturer's  "Pocket  Books"  most  generally  found  in  offices  as  a  basis 
for  the  classification.  Only  distinctive  and  well  marked  differences  have 
been  taken  into  account. 

Summarizing  now  the  values  which  may  be  obtained  from  the 
supplementary  tables.  Each  table  gives: 

(f)  The  percentage  of  uniform  load  in  pounds  per  square  foot  allowable 
on  all  market  shapes  of  the  same  depth  of  I-beams,  channels,  deck-beams, 
and  zees,  other  than  the  standard  weight  section  represented  by  the  diagram. 

Example. — Suppose  for  a  girder  of  20-ft.  span  and  14-ft.  spacing,  it  is 
desired  to  use  a  15-in.  I-beam,  the  load  being  assumed  at  200  Ibs.  per  sq.  ft. 
of  floor.  A  i5-in.,  6o-lb.  beam  will  carry  151  Ibs.  and  the  table  opposite  the 
diagram  for  this  beam  gives  1307%  of  this  value  for  a  15-in.  8o-lb.  beam,, 
which  is  equivalent  to  109  Ibs.  for  the  allowable  load. 

(g)  The  same  percentage  factor  may  be  taken  to  express  the  percentage 
of  the  diagram  values  for  spacing  of  beams  or  girders,  if  it  is  more  con- 
venient to  use  the  diagram  values  for  the  loading. 

Example: — Suppose  for  a  girder  of  2O-ft.  span  and  an  assumed  load  of 
150  Ibs.  per  sq.  ft.  of  floor,  it  is  desirable  to  use  15-in.  beams,  spaced  18^ 
ft.  c.  to  c.  The  spacing  of  15-in.  6o-lbs.  beams  for  the  foregoing  can  only 
be  14^/2  ft,  and  the  table  opposite  gives  130.7%  for  the  15-in.  8o-lb.,  which  is 
equivalent  to  i8^4  ft.  c.  to  c. 

(h)  The  allowable  end  reaction  for  safety  of  the  web  without  re- 
inforcement for  buckling.  (See  also  the  diagrams  for  end  reactions  given 
in  Chapter  VI.) 

DIAGEAMS  FOR  ANGLES  AND  TEES.— The  diagrams  on  an- 
gles and  tees,  Nos.  16  to  21,  will  be  understood  from  the  preceding 

*The  end  reactions  resulting  from  any  uniform  load  can  be  obtained 
directly  from  Diagram  No.  28  without  any  arithmetical  work. 


FLOOR    FRAMING.  15 

description  of  Diagrams  Nos.  i  to  15,  without  any  difficulty.  They 
give  the  relation  between  span,  spacing  and  load  in  exactly  the  same 
way  as  the  diagrams  for  I-beams.  A  table  accompanies  each  of  the 
diagrams  which  gives  the  percentage  factors  for  shapes  of  the  same 
depth  but  of  different  weights  and  width  of  horizontal  flange. 

DIAGRAM  FOR  REDUCING  THE  VALUE  OF  A  CONCEN- 
TRATED LOAD  TO  AN  EQUIVALENT  VALUE  OF  UNIFORM 
LOAD  PER  UNIT  AREA.— The  Diagram  No.  22  shows  for  any 
area  of  floor  tributary  to  a  beam,  the  uniform  load  per  square  foot 
which  is  equivalent  to  a  concentrated  load  of  any  given  amount  in 
the  middle  or  at  any  other  point  on  the  beam. 

The  abscissas,  in  Diagram  No.  22,  represent  floor  areas  in 
square  feet ;  the  ordinates  represent  equivalent  uniform  load  per 
square  foot  of  floor  in  pounds.  The  diagonal  lines  represent  con- 
centrated loads  in  pounds.  The  scale  of  ordinates  changes  for  a 
change  in  the  position  of  the  load  along  the  beam.  The  position 
of  the  load  is  expressed  as  a  fraction  of  the  span,  and  ordinate  scales 
for  different  values  of  this  fraction  are  given  to  the  right  of  the 
diagram.  In  any  particular  problem,  the  proper  scale  of  ordinates 
is  to  be  selected  from  these.  The  ordinate  scale  at  the  left,  to 
which  the  main  diagram  is  drawn,  is  for  a  load  at  the  middle  of  the 
span. 

To  use  the  diagram  take  an  abscissa  equal  to  the  floor  area 
tributary  to  the  beam,  and  follow  up  to  the  diagonal  line  represent- 
ing the  concentrated  load.  Select  the  proper  ordinate  scale  for  the 
position  of  the  load  and  read  the  equivalent  uniform  load.  This 
is  to  be  added  to  the  normal  uniform  load  on  the  floor,  and  this  sum 
used  as  load  in  referring  to  Diagrams  Nos.  I  to  21.  In  case  the 
position  of  the  load  is  not  represented  exactly  by  any  ordinate 
scale,  use  the  nearest  one  or  interpolate. 

Example. — Suppose  a  post  from  a  stair  platform  carries  10,000  Ibs.  to 
a  point  4  ft.  from  the  end  of  a  20-ft.  girder;  suppose  one-half  the  sum  of  the 
spans  of  the  beams  framing  into  the  girder  is  20  ft.,  thus  giving  400  ft.  tribu- 
tary floor  area  upon  which  the  normal  live  and  dead  load  is  160  Ibs.  per 
sq.  ft. 

The  diagram  gives  32  Ibs.  per  sq.  ft.  for  a  load  concentrated  V«» 
of  the  span  from  the  end.  Thus  it  is  necessary  to  design  this  girder  for  a 
uniform  load  of  192  Ibs.  per  sq.  ft.  A  20-in.  65-lbs.  I-beam  was  strong 
enough  for  the  normal  loading,  while  the  added  concentrated  load  calls  for 
a  2O-in.,  8o-lbs.  I-beam. 

The  end  reaction  should  be  taken  as  half  the  sum  of  the  nor- 


l6  STRUCTURAL    DESIGNERS'    HANDBOOK. 

mal  uniform  load  and  the  equivalent  uniform  load  (equal  to  J  total 
uniform  load  times  floor  area  carried).  The  result  so  obtained  is 
a  trifle  too  high,  but  the  error  is  on  the  safe  side. 

TABLES  OF  PROPERTIES  OF  SHAPES.— It  will  be  proper  here 
to  again  refer  to  the  scries  ol  tables  in  Chapter  VIII,  which  give 
the  properties,  including  the  section-moment  for  all  the  standard 
and  special  structural  shapes  of  steel.  These  tables  can  be  used  for 
a  variety  of  purposes.  The  section-moments  will  be  particularly 
useful  for  beam  design.  Thus,  when  an  I-beam  has  been  specified 
and  it  is  desired  to  use  a  channel  in  its  stead,  the  section-moments 
given  in  these  tables,  can  be  used  to  find  one  that  has  an  equivalent 
strength  to  the  one  specified.  For  instance,  if  a  Q-in.  2i-lb.  beam 
was  called  for,  then  from  the  tables  it  will  be  seen  that  a  12-in.  2oJ- 
Ib.  channel  will  carry  the  same  load,  or  if  it  is  to  carry  only  half  the 
load,  a  9-in.  13-lb.  channel  will  be  satisfactory. 


Diagrams  \  to  15 

For  I-Beams  and  Channels,  with  Supplementary  Tables 


Diagrams  16  to  2  J 
For  Angles  and  Tees 


Diagram  22 

For  Reducing  the  Value  of  a  Concentrated  Load  to 
an  Equivalent  Value  of  Uniform  Load 


i8 


STRUCTURAL    DESIGNERS'   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  3=in.  x  5.5  Ib.  I=beams  in  Ibs.  per 
sq.  ft.  of  floor. 

(£)   The  allowable  spacing-  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load, 
(c)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing, 
(c?)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 

(^)    The  percentage  of   load  allowable    for   any    unsupported   length   of   top 
flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(/")  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 
standard. 

(£-)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(//)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 
buckling. 


3"! 
Beams 

Carnegia.  Cambria, 
Jones  &  Laughlins 
Phoenix 

1 
Fencoyd 

Fassaic 

. 

<D      "o 

o 

. 

c    .    ^ 

o 

0      "o 

0 

SI 

CD  Ui 

|| 

||| 

y 

£  c~S 

O  CD  eg 

ll 

ll 

111 

_O  ®  03 

4 

(K  fl 

2^,2 
gac 

^T3  ^t 

0  d  o3 
^  O  3 

y 

Is! 

5 

^S? 

5    8        £ 

<"S 

<J       * 

1            * 

3£l 

<3  M 

Lbs. 

Ins. 

*w. 

Tons  !     Ins. 

%w. 

Tons 

Ins. 

xw. 

Tons 

5-5 

0.17 

100 

2-3 

0.17 

97 

2-3 

6-5 

0.26 

108 

3-5 

0.24 

1  06 

3-2 

7-5 

0.36 

116 

4-8 

0-34 

«s 

4-6 

3 

CHAN 

NELS 

4 

0.17 

65 

2-3 

0.17 

65     i    2.3 

5 

0.26 

71 

3-5 

i    0-25 

7'     i    3-4 

6 

0.36 

82 

4-8    ! 

0-35 

82 

4-7 

3 

ZEES 

6.7 

0.25 

"3 

8-4 

0.31 

140 

9-7 

0-37 

i5i 

FLOOR    FRAMING. 


Diagram  No*  \ 


3-in*  x  5.5-lb*  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
S  6  7          &         9        10 


-       O 


-       O 


4  &  6  7          0        2       »0  15 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


20 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  4=in.  x  7.5  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(6)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(c)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(cT)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 

(<?)  The  percentage  of  load  allowable  for   any    unsupported    length    of   top 
flange  in  feet. 

THE  TABLE-  FOLLOWING  GIVES  : 

(/ )  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(^•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(A)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


4"! 
Beams 

Carnegrie,  Cambria, 
Jones  &  Lautjhlins, 
Phoenix 

Pencoyd 

Passaic 

11 

Lbs. 

Web 
thickness. 

Allowable 
load  pet- 
square  foot. 

Allowable 
end 
reaction. 

Web 
thickness. 

Allowable 
load  per 
square  foot. 

Allowable 
end 
reaction. 

Web 
thickness. 

Allowable 
load  per 
square  foot. 

Allowable 
end 
reaction. 

Ins. 

%  W. 

Tons 

Ins. 

%W. 

Tons. 

Ins. 

%  W. 

Tons 

60 

7-5 

0.18 

O.20 

77 
98 

3-2 
3-6 

0.19 

IOO 

3-4 

0.19 

IOO 

3-4 

8-5 

0.26 

107 

47 

0.24 

107 

4-3 

9-5 

IO.O 

10.5 

0-34 

112 

6.1 

0.32 

112 

5-8 

0.39 

114 

7.0 

0.41 

118 

7-4 

0-39 

118 

7.0 

4  " 

5-o 

5-25 
6.0 
6.25 

CHAN 

NELS. 

0.17 
0.24 

60 
67 

"^.O 

4-3 

0.18 

64 

3-2 

0.18 

64 

3  2 

0.25 

70 

4-5 

0.24 

70 

43 

7-25 
8.0 

IO.O 

4  " 

0.32 

77 

5-8 

0.32 

77 

5-8 

0.27 
0.42 

9i 
104 

4-8 

7-5 

ZEES 

8.2 

0.25 

105 

10.3 

0.31 

130 

12.4 

0-37 

155 

FLOOR    FRAMING. 


21 


Diagram  No.  2  4-in.  x  7.5-lb.  I-Beams 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
3  4  5  6          7        &      9       \0  \5 


-    o 


=      cc 


r-J     o 


4  ^6739      10  15 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


STRUCTURAL    DESIGNERS'    HANDBOOK'. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  tmiform  load  on  5=in.  x  9.75  Ib.  I=b earns  in  Ibs.  per 

sq.  ft.  of  floor. 
(£)   The  allowable  spacing  C.  to  C.  in  ft.  for  any   span  and  any  uniform  load. 

(c)  The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 

(d)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 

(e)  The  percentage  of  load  allowable  for   any    unsupported    length    of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES : 

The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


5"! 

Beams 

Carnegie,  Cambria, 
Jones  &  Lauerhlins, 
Phoenix 

Pencoyd 

Passaic 

°3  ^ 
^  o> 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

£*•§ 

•3£S 

|li 

*  s? 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

J®1 

Lbs. 

Ins. 

%  W. 

Tons 

Tns. 

%  w. 

Tons 

Ins. 

#W. 

Tons 

9-75 

0.21 

IOO 

4-7 

0.21 

IOO 

4-7 

0.21 

IOO 

47 

12. 

O   "7  A 

114 

7  6 

12.25 

0.36 

113 

8.1 

0-34 

113 

7.6 

13. 

0.26 

I  ~"  I 

c  8 

14-75 

0.50 

127 

II.  2 

0.49 

127 

II.  O 

15.0 

0.38 

141 

8.5 

I 

5  " 

CHAN 

NELS 

6  o 

o  18 

CJ. 

4O       1 

6-S 

0.19 

63 

4-3 

0.19 

03 

4-3    1 

8  o 

o  70 

64 

6  7 

9.0 

0-33 

73 

7-4 

0.32 

73 

7.2 

0.25 

81 

56 

IO.O 

O  71 

86 

7  o 

0.48 

88 

10.8 

o.47 

88 

10  6 

12  O 

O  47 

96 

O  7     1 

5  " 

ZEES 

n.  6 

0.31 

in 

13-9 

0-37 

133 

16.4 

0.44 

155 

5  " 

BULB 

ANGLE 

I 

10. 

0.31    j         85 

i 

1 

FLOOR    FRAMING. 


Diagram  No,  3 


5-in.  x  9.75-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
5  G          7         8       9       \0 


sr 
LU 

Q 

oc 
o 

QC 

o 


&        e       r      e     9    \o  & 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4Ooth  of  the  span. 


STRUCTURAL    DESIGNERS'    HANDBOOK:. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load on  6=in.  x  12.25  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(6)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load, 
(c)    The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(a?)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 
\e}  The  percentage  of  load  allowable  for   any    unsupported    length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(/")  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(g-)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(h)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


6"! 

Beams 

Carnegie,  Cambria, 
Jones  &  Lauerhlins, 
Phoenix 

Pencoyd 

Passaie 

®  tj"o             ® 

co 

0        4J 

o 

03 

<D      *» 

O 

£"0 

•°1 

IP 

u 

•§1 

||S 

AS 

3  oj 

•3*2 

^0 

||| 

o§a 

£i 

l>  0 

III 

l§l 

^0 

|^S 

ggo 

£% 

•3 

5    Z 

5 

<1  - 

£ 

^1 

3    2 

Lbs. 

Ins. 

%  W. 

Tons 

Ins. 

%W. 

T  JES 

Ins. 

ox  yT 

Tons 

12  O 

O  22 

OQ 

5Q 

12.25 

0.23 

IOO 

6.2 

0.23 

IOO 

6.2 

•y 

14-75 

0-35 

no 

9-4 

0-34 

III 

9.2 

I5.O 

0.25 

121 

6  7 

17.25 

0.48 

119 

12.9 

0.46 

122 

12.4 

17.  c 

O  3  *7 

131 

IO  O 

20.  o 

0.50 

141 

13  5 

6  " 

CHAN 

NELS. 

8 

O.2O 

59 

5-3 

O.2O 

59 

5.3 

O.2O 

58 

5-3 

Q 

0.2? 

62 

6  7 

IO 

o  30 

66 

8  i 

105 

0.32 

69 

8.6 

0.27 

75 

7-3 

12 

0.28 

85 

7  c, 

13 

0.44 

80 

ii  9 

O.4O 

85 

10.8 

o-33 

89 

8.9 

JC 

o  43 

07 

ii  6 

0.56 

89 

I5-I 

0.52 

96 

14.0 

17 

o  38 

116 

IO.2 

18 

O  d3 

I2O 

ii  6 

20 

o<53 

128 

14.3 

6  " 

ZEES 

15.6 

0-37 

n5 

18.3 

044 

134 

21.0 

0.50 

153 

6' 

DECK 

BEAMS 

14.1 

0.28 

84 

17.2 

0-43 

99 

6 

BULB 

ANGLES 

12.3 

0.31 

78 

13.8 

038 

90 

17.2 

0.50           104 

FLOOR    FRAMING.  2$ 

Diagram  No.  4  6-in.  x  J2.25-lb.  I-Beams 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


9        \o 


15 


30 


X 

8 

fc« 

UJ 

u. 
z 

CO 

Q 

en 
O 
DC 
0 

i 

UJ       Q 

\ 

\ 

L 

V 

•.. 

N  POUNDS  PER  SQUARE  FOOT  OF  FLOOR 

\ 

A 

'  1 

^ 

A' 

\   \ 

\ 

\ 

\ 

\ 

V 

\ 

^ 

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> 

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\  !N 

\ 

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SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


26 


STRUCTURAL    DESIGNERS'    HANDBOOK 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The   allowable  uniform  load  on  7=in.  x   15  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(£)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(c)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
( rf)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 

(e)  The  percentage  of  load  allowable  for   any    unsupported    length    of   top 
flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES : 

CO  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(^)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(Ji)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


7"! 

Beams 

Carnegie,  Cambria, 
Jones  &  Lautjhlins, 
Phoenix 

Pencoyd 

Passaic 

<D      +> 

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%w. 

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15 

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100 

7-9 

0.25 

101 

7-9 

0.23 

102 

6.9 

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109 

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0.46 

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BEAMS 

18.1 

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93 

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112 

7" 

BULB 

ANGLES 

16 

0.34 

84 

18.3 

0.44 

92 

FLOOR    FRAMING. 


Diagram  No*  5  7-in,  x  f  5-lb.  I-Beams 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
7         &       9      lo  15  20 


10  15  20 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


28 


STRUCTURAL    DESIGNERS'    HANDBOOK 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  8=in.  x   18  Ib.  I=beams  In  Ibs.  per 

sq.  ft.  of  floor. 
(&)   The  allowable  spacing  C.  to  C.  in  ft.  for  any   span  and  any  uniform  load. 

(c)  The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 

(d)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 

(e)  The  percentage  of  load  allowable  for   any    unsupported    length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(/")  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(^r)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(A)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


8"! 

Beam^ 

Carnegie,  Cambria, 
Jones  &  Lausrhlins, 
Phcenix 

Pencoyd 

Passaic 

03 

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86 

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0.47 

99 

8" 

BULB 

ANGLE 

19-3 

0.41 

82 

FLOOR    FRAMING. 


Diagram  No.  6 


8-in.  x  J8-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
7          &       9       10 


30 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


30 


STRUCTURAL    DESIGNERS'    HANDBOOK 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The   allowable  uniform  load  on  9=in.  x  21   Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(£)   The  allowable  spacing-  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(V)    The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 

(d)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 

(e)  The  percentage  of  load  allowable  for   any    unsupported    length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(_/)  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(^•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(1i)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


9"  I 

Beams 

Carneprie,  Cambria, 
Jones  &  Lausrhlins, 
Phoenix 

Pencoyd 

Passaic 

"SS 

ll 

Allowable 
load  per 
square  foot 

Allowable 
.end 
reaction 

Web 

thickuess 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

| 

|| 

Allowable 
load  per 
square  foot 

AJlowablo 
end 
reaction 

Lbs. 

Ins. 

*W. 

Tons 

Ins. 

#W. 

Tons 

Ins. 

KW. 

Tons 

21 

0.29 

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10.5 

0.29 

IOO 

10.5 

0.27 

99 

9.1 

23.3 

o.  ^c 

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14  2 

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16.6 

0-39 

109 

15.8 

0.40 

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16.2 

27 

0.31 

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II-9 

30 

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23.1 

0.56 

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22.7 

0.41 

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DECK 

BEAM 

26 

0.44 

94 

3° 

0-57 

104 

9  " 

BULB 

ANGLE 

21.8 

0-44 

77 

FLOOR    FRAMING. 


Diagram  No.  7  9-in.  x  2Mb.  I-Beams 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
6  7         8>        9      10  15  20 


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SPAN  OF  BEAMS  OR  GIRDERS  IN   FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


STRUCTURAL    DESIGNERS'   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  !0=in.  x  25  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(£)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(/:)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing, 
(a?)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 
(*?)    The  percentage  of   load  allowable    for   any    unsupported   length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(_/)  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(^•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(A)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


10"! 

Beams 

Carnegia,  Cambria, 
Jones  &  Laughlins, 
Phoenix 

Pencoyd 

Passaic 

-u-*^ 

§1 

£1 

Web 

thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
Joad  per 
square  foot 

Allowable 
end 
reaction 

Lbs. 

Ins. 

#W. 

Tons 

Ins. 

%W. 

Tons 

Ins. 

%W. 

Tons 

25 

0.31 

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12.  0 

0.31 

100 

12.0 

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0.37 

104 

164 

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10  " 

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BEAMS 

27-3 

0.38 

88 

35-7 

063 

105 

10  " 

BULB 

ANGLES 

26.5 

0.48 

82 

32.0 

0.63 

89 

Diagram  No.  8 


FLOOR    FRAMING.  33 

JO-in.  x  25-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

7  S>         9         \0  \5>  20 


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SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4.ooth  of  the  span. 


34 


STRUCTURAL    DESIGNERS'   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  loadon  12=in.  x  31.5  Ib.  I=beamsinlbs.  per 

sq.  ft.  of  floor. 

(6)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(V)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(<a?)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 
(^)    The  percentage  of   load  allowable   for   any   unsupported   length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES: 

(/)  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(,,»•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(Ji)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


12"! 
Beam!- 

Carnegie,  Cambria, 
Jones  &  Lausrhlins, 
Phoenix 

Pencoyd 

Passaic 

•4^-W 

II 

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thickness 

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reaction 

Lbs. 

Ins. 

%  W. 

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Ins. 

%  W. 

Tons 

Ins. 

%w. 

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3*-5 

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83 

3r-3 

40 

0.76 

9i 

41.1 

0.62 

104 

33  5 

ii#  " 

DECK 

BEAMS 

32.2 

0.42 

76 

37.0 

o-55 

85 

FLOOR    FRAMING. 


35 


Diagram  No*  9  J2-in.x  3J«5-lb.  I-Beams 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
~.*>  7  &         »        \0  15  ZO  25  30 


!D 


Q 

gc 
o 

tr 
O 

CO 

< 

UJ 

CQ      Q 


UJ 


UJ 


v  \  \\\\  \\ViWAteVs\Ji\  \  US'.  \.  \f  fv  «Ajj-Xi 
-\  \  \\\OA\V\  :\\TX1\\\'\  \  \^vf\    \  ^ 


\\  \  \\ 


\\\\\\\\\\\\N\\ 


r\\\\ 


\\\\ 


\\\\ 


\\\\\\\ 


V 


\ 


-V-V 


\.    \ 


\    \ 


\\\\  \\ 


\\\\\\\\\ 


\\\\\\\\\ 


\\v 


\  \ 


\-\ 


\\ 


\ \ 


\A 


\'\ 


\  \ 


\\\ 


v\ 


\  \ 


\\ 


\\\ 


A-X 


XX 


\V 


V 


\\ 


\\ 


,p\ 


x\ 


s 


v 


\\ 


\\ 


\\\ 


\\ 


\v 


\ 


\\ 


\\\\\ 


\\ 


P       lo  i&  20 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


CQ 


Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


36 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on   12=in.  x  40  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(£)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span   and  any  uniform  load. 
(c)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(of)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 
(ji)  The  percentage  of  load  allowable  for   any    unsupported    length    of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(f )  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(^•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(A)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


12"! 
Beams 

Carnegie,  Cambria, 
Jones  &  Laughlms, 
Phoenix 

Pencoyd 

Passaic 

4J-g 

SI 

C  SH 
£ft 

Lbs. 
40 

•gl 
£1 
2 

%3 

Ins. 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

o 

y 

£  &  3 

•^           *H 

Tons 

%W. 

Tons 

Ins. 

%W. 

Tons 

Ins. 

%W. 

0.46 

ICO 

24.9 

0.42 

1  02 

22.1 

0-39 

104 

19-3 

45 

0.58 

106 

31-3 

0-54 

109 

29.2 

0.51 

no 

27.6 

50 

0.70 

"3 

37-8 

0-55 

123 

29.7 

0.64 

118 

34-6 

55 
60 

65 

12" 

20 
20.5 
23 
25 
27 

30 

33 
35 

0.82 

119 

44-3 

0.56 
0.68 
0.80 

137 
143 
150 

30-3 
36.8 

43-2 

0.63 

o-75 
0.88 

0.28 

o-35 
0.40 
0.38 
0-45 
0-53 
0.58 

133 
139 
146 

46 

50 
53 
60 
64 
68 
70 

34-0 
40.5 
47-5 

8-5 

15.6 
20.3 
18.4 

24-3 
28.6 

31-3 

CHAN 

NELS 

0.28 

48 

8.5 

0.28 

48 

8-5 

0-39 

54 

19-3 

0-39 

54 

19-3 

0.51 

60 

27.6 

0.51 

60 

27.6 

0.64 

67 

34-6 

0.50 

77 

27.0 

40 

0.76 

73 

41.1 

0.62 

83 

33-5 

FLOOR    FRAMING. 


Diagram  No*  JO 


37 
J2-iru  x  40-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
9       \&  \S>  20 


--     cc 


^      10  IB  20 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


STRUCTURAL    DESIGNERS^   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

O)  The  allowable  uniform  load  on  15=in.  x  42  Ib.  I=beams  in  Ibs.  per 
sq.  ft.  of  floor. 

(&)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(V)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(d)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 

0)    The  percentage  of   load  allowable    for   any   unsupported   length   of   top 
flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(/")  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 
standard. 

(,£-)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(7z)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 
buckling. 


15"! 
Beams 

Carnegie,  Cambria, 
Jones  &  Laughlins, 
Phoenix 

Pencoyd 

Passaic 

.11 

<D  t-t 

££ 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 

thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Lbs. 

Ins. 

%W. 

Tons  |j    Ins. 

%W. 

Tons 

Ins. 

KW. 

Tons 

42 

0.41 

IOO 

19.1 

0.41 

IOO 

19.1 

0.40 

97 

17.7 

45 

0.46 

103 

25-5 

0.45 

104 

24-3 

0.46 

IOI 

25.5 

50 

0.56 

109 

37-2 

0.48 

117 

28.1 

0-45 

120 

24-3 

55 

0.66 

116 

44.6 

0.58 

123 

39-2 

0-55 

126 

36.2 

15  " 

CHAN 

NELS 

33 

0.40 

70 

17.7 

i   0.40 

7i 

17.7 

;  0.40 

69 

17.7 

35 

0.43 

72 

21.8 

0.42 

73 

20  3 

0.44 

71 

23.0 

40 

0.52 

79 

32.8 

0.52 

79 

32.8    |   0.54 

77 

34-8 

45 

0.62 

85 

41.9 

0.62 

85 

41.9    I   064 

84 

43-2 

50 

0.72 

91 

48.7 

0.63 

IOO 

42.6       0.73 

90 

49-3 

55 

0.82 

98 

55-4 

0.72 

1  06 

48.7 

FLOOR    FRAMING. 


39 


Diagram  No.  \\ 


J5-in.x42-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

f5  20  25  30  -40 


m    ^ 


tfi 


LJ 


N&M&^A-t^b.ifeM 


vV\ 


\\\ 


\ 


B\\m^ 


ffc&NX 


\\\ 


\ 


\\ 


\ 


\\ 


\\ 


\\v 


\\\ 


\\ 


\\\ 


\\ 


\\j\\ 


\\\\A 


\\V 


TOZi^F 


10 


vfr* 


iXX 


\    V 


\  \ 


\\ 


\\ 


XY 


\  \ 


x^ 


r^ 


\\ 


^^ 


ss 


\  \ 


\\ 


vi 


\\ 


« 


^\\ 


X 


S*2 


^X 


S3 


F_.-^r^..E-=\nraa3i^s 

Ll 1  \  \\\  KM\W\U\\ 


\\\ 


\\ 


\\N 


\\\\ 


^ 


ii.3 


mn 


\\\ 


k 


4> 


15  20  25  30  -4o 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


LU 


UJ 


50 


Safe  loads  gfiven  include  weig-ht  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


40 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on   15=in.  x  60  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(£)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform   load. 
(c)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(</)  The  weight  of  steel  in  Ibs.    per  sq.  ft.  of  floor. 
(>)  The  percentage  of  load  allowable  for   any    unsupported    length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(/)  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 

standard. 

(£>•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(A)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 

buckling. 


15"! 
Beams 

Carnegia,  Cambria, 
Jones  &  Laughlins, 
Phoenix 

Pencoyd 

Passaic 

f! 

Web 
thickness 

||| 
^1 

Allowable 
end 
reaction 

Web 
thickness 

\0  Allowable 
load  per 
j^  square  foot 

Allowable 
end 
reaction 

Web 

thickness 

\0  Allowable 
5  load  per 
<J<  4)  square  foot 

Allowable 
end 
reaction 

Lbs. 
60 

Ins. 

%W. 

Tons 

Ins. 

Tons 

Ins. 

0.52 

Tons 

0-59 

ICO 

39-9 

°-55 

102 

36.2 

32.8 

65 

0.69 

104 

46.6 

0.65 

1  06 

43-9 

0.62 

109 

41.9 

70 

0.78 

109 

52.7 

0.63 

118 

42.6 

0.72 

114 

48.7 

75 

0.88 

114 

59-4 

o-73 

122 

49-3 

0.81 

118 

54-7 

80 

0.81 

i3i 

54-7 

0.83 

127 

56.1 

0.91 

123 

61.5 

85 

0.89 

134 

60.  i 

90 

0.99 

139 

66.9 

95 

1.09 

H3 

73-6 

ICO 

1.18 

148 

79-7 

15  " 

CHAN 

NELS 

33 

0.40 

51 

17.7 

0.40 

51 

17-7 

0.40 

50 

17.7 

35 

0-43 

53 

21.8 

0.42 

53 

20.3 

0.44 

52 

23.0 

40 

0.52 

57 

32.8 

0.52 

57 

32-8    , 

0-54 

56 

34-8 

45 

0.62 

62 

41.9 

0.62 

62 

41-9    ! 

0.64 

61 

43-2 

5° 

0.72 

66 

48-7 

0.63 

72 

42.6 

0-73 

65 

49-3 

55 

0.82 

71 

55-4 

0.72 

77 

48.7 

j 

FLOOR    FRAMING. 


Diagram  No.  J2 


J5-in.  x  60-flb.  I-Beams 


* 


10 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
15  20  3O 


40         , 


\~-       O 
=      O 


QC 

—  =         UJ 
-    -          Q. 


UJ 

Q 

E     — 

E       CD 


s    < 

UJ 
CO 

_j 

UJ 
UJ 

t- 

co 


20  2^          30 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i~4OOth  of  the  span. 


STRUCTURAL    DESIGNERS'   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  18=in.  x  55  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 
(&)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 

(c)  The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 

(d)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 

(e)  The  percentage  of   load  allowable    for   any   unsupported   length   of   top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES  : 

(/")  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 
standard. 

(^•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(/*)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 
buckling. 


IS"  I 
Beams 

Carnegie,  Cambria, 
Jones  &  Laughiins, 
Phoenix 

Pencoyd 

Passaic 

•%»1S 

P 

is 

Lbs. 

•si 

EM3 

£ 

Ins. 

Allowable 
load  per 
square  foot 

H  Allowable 
end 
£  |  reaction 

£  Web 
»  thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 

thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

%W. 

%W.    i  Tons 

Ins. 

%W. 

Tons 

55 

0.46 

IOO 

22.4  |     0.46 

lol      i    22.4 

0.47 

101 

23-8 

60 

°-55 

106 

36.2       0.54 

107        34-5 

o-55 

106 

36.2 

65 

0.64 

in 

49.4  |     0.63 

112 

47-7 

0.64 

in 

49-4 

70 

75 
80 

85 
90 

0.72 

116 

58.3 

0.62 
0.71 
0.79 
0.74 
0.82 

123 
128' 

133 
144 
149 

46.2 

57-5 
64.0 

59-9  ! 
66.4 

0.65 
0.62 

0.70 

122 

137 
142 

50.5 
46.2 

56.7 

.... 

.... 

I 

FLOOR    FRAMING. 


43 


Diagram  No.  J3  J8-in.x  55-lb.  I-Beams 

SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

20  30  4o  So 


H-    o 
o 


UJ 


|C\ 


10 


AO 


50 


\5  20  25  30 

SPAN  OF  BEAMS  OR  GIRDERS  IN   FEET 

Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


STRUCTURAL    DESIGNERS'   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  20=in.  x  65  Ib.  I=beams  in  Ibs.  per 
sq.  ft.  of  floor. 

(&)   The  allowable  spacing-  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load, 
(c)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing, 
(c?)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 

(>)    The  percentage  of   load  allowable    for   any   unsupported   length   of   top 
flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES : 

(_/")  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 
standard. 

(  g)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(A)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 
buckling. 


20"! 
Beams 

Carnegie,  Cambria, 
Jones  &  Laughlins, 
Phoenix 

Pencoyd 

Passaic 

§•2 

n 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

1-1 

Web 
thickness 

g    •§ 

S£<2 
gft® 

^1 

Allowable 
end 
reaction 

Lbs. 

Ins. 

*W. 

Tons 

Ins. 

*W. 

Tons 

Ins. 

%W. 

Tons 

65 

0.50 

IOO 

25.0 

0.50 

IOO 

25.0 

0.50 

99 

25.0 

70 

0-57 

104 

38.5 

0.56 

105 

38.5 

0-57 

102 

38.5 

75 

0.65 

109 

50-5 

0.64 

109 

48.6 

0.66 

1  06 

51-7 

80 

0.60 

125 

41.8 

0.63 

120 

46.6 

0.69 

115 

56.6 

85 

0.66 

129 

51-7 

0.70 

124 

54-5 

0.76 

II9 

66.9 

90 

0.74 

133 

64.0 

0.78 

128 

57-8 

0.78 

I29 

70.2 

95 

0.81 

137 

72.9       0.74 

137 

68.5 

IOO 

0.88 

142 

79.2 

0.81 

141 

76.5 

i 

FLOOR    FRAMING. 


45 


Diagram  No*  J4 


20-in.  x  65-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 

15  20  25  Z>0  AO 


CO 

DC 
LU 
Q. 

05 
Q 

z 
=> 
o 


so 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 


Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


46 


STRUCTURAL    DESIGNERS'   HANDBOOK. 


THE  DIAGRAM  ON  OPPOSITE  PAGE  GIVES  : 

(a)  The  allowable  uniform  load  on  24=in.  x  80  Ib.  I=beams  in  Ibs.  per 

sq.  ft.  of  floor. 

(£)   The  allowable  spacing  C.  to  C.  in  ft.  for  any  span  and  any  uniform  load. 
(<:)   The  allowable  span  in  ft.  for  any  uniform  load  and  any  spacing. 
(<f)  The  weight  of  steel  in  Ibs.  per  sq.  ft.  of  floor. 
0)    The  percentage  of   load  allowable   for   any   unsupported  length   of  top 

flange  in  feet. 

THE  TABLE  FOLLOWING  GIVES : 

(_/)  The  percentage  of  load  allowable  on  special  shapes  other  than  the  above 
standard. 

(^•)  The  same  percentage  factor  to  be  used  for  spacing  instead  of  load. 
(7z)    The  allowable  end  reaction  for  safety  of  web  without  reenforcement  for 
buckling. 


24"! 
Beams 

Carnegia,  Cambria, 
Jones  &  Laughlins, 
Phoenix 

Pencoyd 

Passaic 

II 

<£>  t-i 
£& 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 
thickness 

Allowable 
load  per 
square  foot 

Allowable 
end 
reaction 

Web 

thickness 

Allowable 
load  per 
square  foot 

<D 

M 

oS§ 

3  s 

Lbs. 

Ins. 

%W. 

Tons 

Ins. 

%W. 

Tons 

Ins. 

%W. 

Tons 

80     ! 

0.50 

ICO 

20.4 

0.50 

101 

20.4 

85     |    0.57 

104 

30-9 

0.56 

105     i    24.9 

90 

0.63 

107 

42.3 

0.56 

113     j    29.4 

95         °-69 

in 

54.5       0.62 

116        34.0 

100 

0-75 

114 

66.3 

0.68 

120 

39-9 

FLOOR    FRAMING. 


47 


Diagram  No.  J5 


24-in*  x  80-lb.  I-Beams 


SPAN  OF  BEAMS  OR  GIRDERS  IN  FEET 
*  20  25'  *o'  40 


bo" 


60' 


10 


SPAN  OF 


20' 

BEAMS 


2&'  30'  40' 

OR  GIRDERS  IN  FEET 


30' 


60 


Safe  loads  given  include  weight  of  beam  and  maximum  fiber  stress, 
16,000  Ibs.  per  sq.  in.  maximum  deflection  i-4OOth  of  the  span. 


48 


STRUCTURAL    DESIGNERS'    HANDBOOK 


Diagrams  Nos.    16,    17,    18,    19,   20  and  21 
FOR  GIVING: 

(a)     The  allowable   uniformly  distributed  live  and  dead  load,  on  Angles 
and  Tees,  as  beams  or  girders,  in  pounds  per  square  foot  of  floor. 
(6)     The  allowable  spacing,  center  to  center,  for  any  span  and  any  uniform 
loading. 
(f)     The  allowable  span  in  feet  for  any  uniform  loading  and  any  spacing. 

V 
^  fl 

1 

£ 
^ 

% 

Diagram  No.  16 

i 

2    3 

4 

5 

6 

Section. 

eg 

0) 

^§ 

Ofl 

a 

^StR 

Is 
& 

Ins 
£ 

I 

I 

Height  of  leg 
or  stem 

ickness 

Weight  per 
lineal  foot 

Allowable 
load 
per  sa.  ft 

v\\\ 

V 

5 

\ 

r" 

\\\ 

s  V 

\ 

\ 

^ 

SANA 

\  \ 

\ 

\ 

\ 

v\ 

\\ 

^  > 

1 

\ 

\ 

,£3 

H 

s  SN 

\\\ 

\ 

\ 

\ 

\  V 

s\\ 

\\ 

\ 

\ 

\ 

Ins 

Ins 

# 

tn 

X 

X 

3bs. 

0.6 
0.8 

0.8 

1.2 

i-5 

0.87 
1.23 

%  W. 

\A  ' 

S\\s 

N\ 

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STRUCTURAL    DESIGNERS'    HANDBOOK. 


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52  STRUCTURAL    DESIGNERS'    HANDBOOK, 

Diagram  No.  22 

For  reducing  the  value  of  a  concentrated  load  to  an  equivalent 
value  of  uniform  load  per  unit  floor  area. 


Distance  of  Concentrated  Load 
"C"  from  End  of  Beam  or 
Girder. 


AREAS  IN  SQUARE  FEET 

200  300          400       500 


200  500  400        500 

AREAS  IN  SQUARE   FEET 


1000 


Example. — Suppose  a  post  from  a  stair  platform  carries  10,000  Ibs.  to 
a  point  4  ft.  from  the  end  of  a  20-ft.  girder;  suppose  one-half  the  sum  of  the 
spans  of  the  beams  framing  into  the  girder  is  20  ft,  thus  giving  400  ft.  tribu- 
tary floor  area  upon  which  the  normal  live  and  dead  load  is  160  Ibs.  per 
sq.  ft 

The  diagram  gives  32  Ibs.  per  sq.  ft.  for  a  lo^-d  concentrated  Vio  Ibs. 
of  the  span  from  the  end.  Thus  it  is  necessary  to  design  this  girder  for  a 
uniform  load  of  192  Ibs.  per  sq.  ft. 


CHAPTER  IV.— SPANDREL  BEAMS. 

The  diagrams  and  tables  given  in  Chapter  III  on  beams  used 
in  floor  framing  cover  the  large  majority  of  cases  of  beamwork 
arising  in  building  design.  Numerous  cases  arise,  however,  in 
connection  with  building  work  in  which  beams  are  required  to 
carry  loads  that  are  not  reduced  to  the  same  unit  load  as  in  floor 
design.  These  are  various  but  will  be  classed,  for  convenience, 
under  the  head  of  spandrel  beams. 

Spandrel  beams  carry  a  variety  of  loads  ranging  from  contin- 
uous curtain  walls  and  individual  piers  to  extraneous  loads  from 
balconies  and  the  like.  Two  or  more  of  these  loads  may  be  com- 
bined on  the  same  beam. 

A  system  is  herewith  presented  for  the  design  of  such  beams. 
It  calls  for  a  minimum  expenditure  of  time  and  insures  a  high  de- 
gree of  safety  in  the  solution  of  this  problem.  The  distinguishing 
feature  of  the  system  is  the  method  of  considering  a  concentrated 
load  for  any  position  it  may  have  upon  the  beam.  For  a  load  uni- 
formly distributed  or  a  load  concentrated  at  the  middle  of  a  beam, 
the  system  differs  but  slightly  from  the  ordinary  methods,  as  will 
be  seen  by  referring  to  the  explanation  of  Diagrams  Xos.  24,  25 
and  26. 

As  explained  in  Chapter  I  under  "Loads  on  Beams,"  the  effect 
of  a  load  concentrated  at  any  other  point  than  the  middle  is  less 
than  the  effect  of  the  same  load  if  concentrated  at  the  middle  of  the 
beam.  Evidently  therefore,  there  is  always  an  equivalent  reduced 
load  that  will  have  the  same  effect  on  a  beam  when  concentrated  at 
the  middle  as  the  actual  load  when  concentrated  at  any  other  point. 
This  equivalent  reduced  load  is  given  on  Diagram  No.  23  and  the 
method  of  obtaining  it  will  be  understood  from  the  following: 

EQUIVALENT  LOAD  DIAGRAM.— In  this  Diagram  No.  23, 
the  abscissas  represent  the  position  of  the  load,  and  the  ordinates 
represent  equivalent  load.  The  actual  concentrated  load  is  shown 
as  a  curved  line,  and  the  position  of  the  load  is  given  in  various 
ways.  At  the  top  of  the  diagram  the  abscissa  scale  shows  the  dis- 
tance of  the  load  from  the  end  of  the  beam  as  a  fraction  of  the 

(53) 


54  STRUCTURAL    DESIGNERS'    HANDBOOK. 

span.  At  the  bottom  of  the  diagram  the  distance  from  the  load 
to  the  end  of  the  beam  is  given  in  feet  in  different  scales  for  various 
spans  from  10  to  26  ft.  The  ordinate  scale  gives  the  equivalent 
load  concentrated  at  the  middle. 

To  use  the  diagram,  take  an  abscissa  representing  the  distance 
of  the  load  from  the  end  of  the  beam  (selecting  one  of  the  foot 
scales  for  the  given  span,  or  else  using  the  fraction  scale  at  the 
top  of  the  diagram)  and  follow  up  to  the  curved  line  representing 
the  load.  Follow  the  horizontal  at  the  intersection  reading  equiva- 
lent reduced  middle  concentrated  load. 

The  diagram  also  has  a  horizontal  scale  showing  the  reaction 
at  the  end  nearest  to  the  load,  in  per  cent,  of  the  actual  concen- 
trated load.  This  value  of  reaction  is  to  be  used  in  investigating 
the  end  shear  or  tendency  of  the  web  to  buckle  by  comparing  with 
the  maximum  allowable  end  shear  on  any  beam,  as  given  in  the 
tables  in  Chapter  VIII,  or  as  given  in  the  supplementary  tables  in 
Chapter  III.  The  subject  of  end  reactions  is  treated  more  fully  in 
Chapter  VI. 

DIAGRAMS  FOR  SAFE  LOADS  ON  I-BEAMS  AND  CHANNELS. 
— The  Diagrams  Nos.  24,  25  and  26  are  for  the  design  of  miscel- 
laneous beams  and  girders  conveniently  classed  under  the  head  of 
spandrel  beams.  If  time  was  not  an  important  item  in  the  design 
of  beamwork,  these  diagrams  could  take  the  place  of  those  preced- 
ing them,  for  they  are  adapted  for  general  application. 

The  method  of  using  these  diagrams  will  be  clear.  In  each  of 
the  three  diagrams,  the  abscissas  represent  span  of  beam  in  feet, 
while  the  ordinates  represent  uniform  total  load,  or  total  load  con- 
centrated at  the  middle.  The  diagonal  lines  represent  the  different 
sizes  of  I-beams  and  channels.  The  smaller  sizes  of  I-beams  are 
shown  on  Diagram  No.  24,  while  the  larger  sizes,  i5-in.  and  over 
are  shown  on  Diagram  No.  25.  All  sizes  of  channels  are  shown  on 
Diagram  No.  26.  The  heavy  full  diagonal  lines  on  these  diagrams 
show  the  "standard"  sections  of  different  sizes ;  the  light  full  line 
show  the  special  sections.  As  will  be  understood,  the  change  in 
direction  of  the  lines  is  due  to  the  deflection  entering  as  a  limiting 
factor  above  a  certain  span.  The  reason  for  the  presence  of  dotted 
lines  parallel  to  these  lines  will  be  given  in  Note  2. 

In  these  diagrams  also,  the  left  hand  portion  of  the  lines,  that  deter- 
mined by  the  allowable  fiber  stress,  is  continued  as  a  dotted  line  beyond  the 
point  where  deflection  enters  as  a  factor.  This  dotted  continuation  can  be 
used  when  a  beam  is  to  be  designed  without  reference  to  deflection. 


SPANDREL    BEAMS.  55 

To  use  the  diagrams  take  an  abscissa  equal  to  the  span,  the 
ordinate  (on  the  proper  scale,  either  for  load  uniformly  distributed 
or  concentrated  at  the  middle)  equal  to  the  load,  and  the  section  to 
be  used  is  read  off  on  the  diagonal  at  the  intersection.  Obviously, 
the  diagram  may  also  be  used  to  give  maximum  load  or  maximum 
span  for  any  given  section  of  I-beam  or  channel,  on  a  given  span 
or  under  a  given  load,  respectively. 

NOTE  i. — The  special  15-in.  I-beams  run  up  among  the  i8-in.  and  2O-in. 
I-beams,  but  to  discriminate  it  is  onlv  necessary  to  note  the  point  of  de- 
flection of  the  lines.  The  same  rule  applies  to  the  diagram  for  channels. 

NOTE  2. — If  the  loads  on  a  beam  or  girder  consist  of  comparatively 
light  concentrations  on  top  of  a  well  distributed  uniform  load,  it  is  advisa- 
ble to  reduce  the  concentrated  loads  to  an  equivalent  uniform  loading. 
The  reason  for  this  will  be  evident  from  the  following:  As  the  span  in 
inches  of  a  steel  beam  which  is  uniformly  loaded  increases  above  21.75  times 
its  depth  in  inches,  the  maximum  fiber  stress  begins  to  decrease  from 
16,000  Ibs.  per  sq.  in.  if  designed  for  a  limiting  deflection  of  one  four-hun- 
dredth of  the  span.  In  the  case  of  a  load  concentrated  in  the  middle,  the  de- 
crease does  not  begin  to  take  place  until  the  span  is  27.2  times  the  depth,  or 
il/4  times  that  for  uniform  loading. 

On  Diagrams  Nos.  24,  25  and  26,  this  difference  in  safe  deflection  is 
shown  graphically  by  dotted  lines  for  beams  with  uniform  loading  and  by 
full  lines  for  beams  with  load  concentrated  in  the  middle. 

NOTE  3. — When  large  concentrated  loads  occur  at  both  ends  of  a 
beam  the  diagrams  should  not  be  used.  Use  tables  in  Chapter  VIII. 


56  STRUCTURAL    DESIGNERS'    HANDBOOK. 

Equivalent  load  in  tons,  M.  pounds  or  C.  pounds. 


ra 
o 
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o 

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Example. — A  beam  supports  a  load  of  1,000  pounds  (10  C.  or  i  M.)  i 
ft.  from  the  end  of  a  12-ft.  span.  What  equivalent  value  of  load  concen- 
trated in  the  middle  would  require  a  beam  of  the  same  strength?  Answer: 
305  pounds  (3.05  C.  or  0.305  M.). 


SPANDREL    BEAMS. 


57 


Diagram  No.  24* 

For  giving  the  allowable  load  on  standard  and  special  I-beams. 
SPAN   IN  FEET 


SPAN   IN  FEET 


The  deflection  curves  are  shown  by  full  lines  for  loading  concen- 
trated in  the  middle  and  dotted  lines  for  uniformly  distributed;  thus  a 
6-in.  x  i21/4-lb.  beam  with  a  span  of  15  ft.  will  carry  1.15  tons  concentrated 
in  the  middle  or  1.85  tons  uniformly  distributed. 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


Diagram  No.  25 

For  giving  the  allowable  load  on  standard  and  special  I-beams. 
SPAN   IN  FEET 


UrtlFORfl  C" 


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SPAN    IN  FEET 

Example.— A  2O-in.  x  6s-lb.  beam  42-ft.  span  will  carry  7.35  tons  con- 
centrated in  the  middle  of  the  span  or  12.35  tons  uniformly  distributed. 


SPANDREL    BEAMS. 

Diagram  No.  26 


59 


For  giving  the  allowable  load  on  standard  and  special  channels. 
SPAN    IN  FEET 


a 
CO 


o      —  *  — 


SPAN    IN  FEET 

Example. — A  12-in.  x  2O.5-lb.  beam  24-ft.  span  will  carry  2.35  tons  con- 
centrated in  the  middle  of  the  span  or  4.2  tons  uniformly  distributed. 


60  STRUCTURAL    DESIGNERS'1    HANDBOOK. 

CHAPTER  V.— GRILLAGE  BEAMS. 

FOOTINGS. — The  use  of  steel  beams  in  footings  is  a  problem  of 
frequent  occurrence  with  the  structural  designer.  This  chapter 
deals  with  the  design  of  the  steel  beams  for  grillage  footings  and 
presupposes  a  general  acquaintance  with  the  subject  of  founda- 
tions* on  the  part  of  the  reader. 

Grillage  footings  are  in  general  either  footings  of  walls  or  foot- 
ings of  columns.  The  former  are  somewhat  the  simpler  in  design, 
but  their  treatment  is  precisely  the  same  as  that  for  column  foot- 
ings. They  will  therefore  not  be  especially  referred  to  in  the  fol- 
lowing. When  two  or  more  columns  occur  on  a  single  footing 
the  problem,  on  the  other  hand,  becomes  so  complex  that  only 
those  familiar  with  the  mechanics  of  engineering  should  presume  to 
deal  with  it.  The  properties  of  beams  as  given  in  Chapter  VIII 
may  be  used  for  this  latter  case. 

The  known  quantities  in  the  design  of  a  footing  are  the  load 
on  the  column  and  the  allowable  pressure  per  unit  area  on  the  soil 
(or  other  material)  which  supports  the  grillage.  The  area  of  the 
surface  of  a  footing  which  comes  in  contact  with  the  soil  is  found 
by  dividing  the  load  on  the  footing  by  the  allowable  pressure  on  the 
soil. 

The  accompanying  drawing,  Fig.  2,  shows  a  design  of  a  grill- 
age footing  for  a  single  column  having  two  tiers  of  grillage.  From 
this  drawing  the  elements  of  the  design  of  the  different  tiers  of 
beams  may  readily  be  understood.  The  load  on  the  column  is 
transferred  to  the  grillage  by  a  "base,"  of  cast  iron  or  of  steel,  and 
the  size  of  this  base  must  be  known  or  assumed  before  the  grillage 
beams  can  be  designed. 

DESIGN  OF  GRILLAGE  BEAMS. 

BENDING. — As  explained  in  the  short  treatment  on  the  "Con- 
ventional Methods  of  Considering  Loads  on  Grillage  Beams"  in 
Chapter  I  there  are  two  methods  of  designing  these  beams. 

The  most  common  method  is  to  consider  only  the  projecting 
length  of  these  beams  beyond  the  edge  of  the  tier  or  base  imme- 

*For  this  aspect  of  the  subject  such  books  as  Baker's  Treatise  on 
Masonry  Construction;  Kidder's  Building  Construction  and  Superin- 
tendence, Part  I;  and  Patton's  Practical  Treatise  on  Foundations,  and  the 
back  files  of  the  Engineering  News  and  Engineering  Record  should  be 
consulted. 


GRILLAGE    BEAMS. 


61 


diately  above  them.  Within  certain  limits  this  method  will  give 
satisfactory  results.  It  will  always  give  safe  results  if  b/2a  does  not 
exceed  0.3,  where  b  equals  the  breadth  of  the  base  or  tier 
above,  and  a  equals  the  projection  of  the  beams  beyond  the  edge 
of  this  base — (2a  +  b)  equals  the  entire  length  of  the  grillage  beam 
under  consideration. 

The  second  method  is  more  conservative  although  the  follow- 
ing is  a  modification  of  it  by  30%  limit  allowance  for  the  value 


1 

] 

\ 

1 

rf 

s/ 

1 

1 

\ 

7 

M 

1 

I 

j 

._  . 

_.i 

[ 

5  —  c 

I 

5 

fr  

" 

-b- 

Fig.  i 

> 

*---- 

•- 

<x— 

of  the  concrete  in  the  footing.     It  should  be  stated  at  the  outset 
that  Diagram  No.  27  is  to  be  used  for  both  methods. 

When  b/2a  exceeds  0.3  it  is  generally  advisable  to  increase  the 
number  of  beams  found  by  the  first  method.  This  increase  can  be 
made  in  two  ways  : 

(i)  If  d  is  the  distance  center  to  center  of  grillage  beams,  as  found  on 
Diagram  No.  27  (see  explanations  following),  a  and  b  same  as  before,  and  if 
-c  equals  the  new  distance  c.  to  c.,  then 

1.3  a 

(20) 


c  = 


d. 


a  4-  Va 

(2)  If  n  equals  the  number  of  beams  in  the  tier  (found  by  dividing  the 
total  width  of  the  footing  by  d,  as  given  on  the  diagram  by  the  first 
method)  and  x  equals  the  number  required  by  the  second  method,  then 


(21) 


10  a 


These  formulas  will  be  more  fully  illustrated  in  the  example  on 
page  64. 


62  STRUCTURAL    DESIGNERS'    HANDBOOK. 

While  the  bending  is  the  main  item  that  determines  the 
strength  of  grillage  beams,  one  other  determinative  factor  should 
not  be  neglected: 

BUCKLING  OF  THE  WEB. — The  following  is  practically  an 
empirical  method  of  ensuring  the  safety  of  the  webs  of  grillage 
beams  against  buckling.  Here  again  the  concrete  is  undoubtedly 
a  factor  in  the  strength  of  the  webs,  but  as  it  is  probably  very  slight, 
its  influence  is  not  considered.  Tables  in  Chapter  VIII  give  values 
in  tons  per  lineal  foot  of  I-beams  for  the  allowable  load  per  lineal 
foot  that  can  be  placed  on  such  a  beam.  These  values  were  com- 
puted according  to  the  "Code"  on  the  basis  of  the  assumption  that 
the  safe  load  on  the  flange  of  one  lineal  foot  of  beam  could  be 
taken  as  a  safe  unit  working  load  per  foot  for  the  total  length  of 
beams  directly  under  the  base. 

NOTE. — The  flanges  of  nearly  all  rolled  beams  are  usually  a  little 
higher  on  one  side  than  on  the  other,  thus  there  is  a  slight  tendency  for 
eccentricity  of  loading  on  the  web.  It  is  therefore  advisable  to  be  liberal 
in  the  use  of  separators  between  grillage  beams,  especially  directly  under 
the  edges  of  the  tier  above. 

DIAGRAM  FOR  GRILLAGE  BEAMS.— The  make  up  of  Dia- 
gram No.  27  is  quite  simple.  Abscissas  represent  span ;  i.  e.,  pro- 
jecting portion  of  beams  (symbol  "a")  and  ordinates  represent  the 
safe  loads ;  diagonal  lines  represent  the  different  sizes  and  weights 
of  beams.  The  safe  loads  are  expressed  in  tons  per  square  foot  of 
area,  and  therefore  different  ordinate  scales  are  necessary  for  dif- 
ferent spacings  of  beams.  These  suitable  scales  are  shown  at  the 
left  and  right  of  the  diagram,  so  that  8,  10,  12,  14  or  i6-in.  spacing 
of  beams  are  represented — the  scale  given  on  the  diagram  proper 
is  for  12-in.  spacing,  while  the  other  scales  are  found  at  the  sides. 

NOTE  i. — The  loads  on  grillage  beams  vary  inversely  as  the  spacing  of 
the  beams,  for  instance,  suppose  2O-in.  spacing  was  desired,  evidently  half 
the  load  given  in  the  diagram  for  lo-in.  spacing  will  give  the  correct  size 
of  beam  for  2O-in.  spacing. 

NOTE  2. — The  full  heavy  lines  on  the  diagram  are  for  the  standard 
minimum  weight  I-beams,  and  the  fine  lines  for  other  weights.  These  lines 
give  values  on  a  basis  of  16,000  Ibs.  per  sq.  in.  max.  fiber  stress.  The 
dotted  lines  produced  from  the  right  hand  portions  of  the  curves,  at  the 
bend  of  the  curves,  give  values  for  the  standard  minimum  weight  I-beams 
on  a  basis  of  a  fiber  stress  of  20,000  Ibs.  per  sq.  in.  and  a  limiting  deflection 
of  one  five-hundredth  of  the  span. 

NOTE  3. — The  limiting  values  for  the  pressure  on  mortar  and  con- 
crete are  indicated  by  clotted  lines  across  the  diagram.  It  is  advisable  to- 
keep  well  below  these  limits. 


Diagram  No*  27 

For  giving  size,  weight  and  spacing  of  I-beams  necessary  for 
each  of  the  several  tiers  in  a  grillage  footing. 


ToC. 


10 


I2CE/1TRE     TO     CENTRE         OF          GRILLRGE         BEAMS'.  M    INCHES  =I2|   \A 


PROJECTION  OF  GRILLAGE  BEAMS  IN   FEET 

Example. — Grillage  beams  10  ins.  x  25  Ibs.  projecting  3  ft.  and  spaced  8 
ins.  c.  to  c.  are  good  for  5.4  tons  per  square  foot;  10  ins.  c.  to  c.,  4.3  tons; 
12  ins.,  3.6  tons;  14  ins.,  3.1  tons,  and  16  ins.,  2.7  tons.  (See  text) 

(63) 


64  '  STRUCTURAL    DESIGNERS1    HANDBOOK. 

To  use  the  diagram  for  the  design  of  grillage  beams,  take  an 
abscissa  to  represent  the  projection  of  the  beams  in  feet,  an  ordi- 
nate  equal  to  the  load  per  square  foot,  using  either  the  ordinate 
scale  in  the  diagram  proper  or  the  supplementary  scales,  and  fol- 
low to  an  intersection.  The  diagonal  line  nearest  above  this  inter- 
section gives  the  size  and  weight  of  beam. 

In  preliminary  work  several  spacings  of  beams  should  be  as- 
sumed and  the  resulting  size  of  beam  obtained  for  the  conditions 
of  load  and  span  already  determined.  A  rough  calculation  of  the 
weights  of  the  beams  will  then  indicate  the  most  economical  for  the 
design. 

Example. — Suppose  a  grillage  footing  is  to  be  designed  for  a  column 
carrying  a  total  load  of  400  tons,  where  the  soil  will  bear  a  safe  loading  of 
4  tons  per  sq.  ft.;  suppose  the  cast-iron  base  of  the  column  is  4  ft.  square. 
The  bottom  tier  would  then  be  10  x  10  ft.  (100  sq.  ft.  in  area),  and  the  next 
tier  4  x  10  ft.  (40  sq.  ft.),  which  would  give  10  tons  per  sq.  ft.  pressure  upon 
it.  The  projection  of  the  beams  will  be  3  ft.  in  both  cases. 

SOLUTION  BY  IST  METHOD. — Using  Diagram  No.  27.  The  beams  re- 
quired for  a  span  of  3  ft.  and  4  ton  loading  may  be  lo-in.  25-lb.  Is,  spaced 
about  lo-in.  c.  to  c.,  giving  12  beams  to  the  tier,  or  12-in.  31^  Ib.  Is  spaced 
about  i6-in.  c.  to  c.,  giving  8  beams  to  the  tier.  Thus  2,560  Ibs.  of  steel  is 
needed  if  12-in.  beams  are  used,  and  3,000  Ibs.  if  the  lo-in.  are  used. 

For  the  next  tier,  i5-in.42-lb.  Is  can  be  spaced  lo-in.  c.  to  c.,  i.e.,  5  beams 
are  required  (2,100  Ibs.),  or  i8-in.  55-lb.  Is,  spaced  i6-in.  c.  to  c.,  i.  e.,  3 
beams  (2,200  Ibs.)  to  the  tier. 

SOLUTION  BY  2D  METHOD. — (A)  Using  formula  (20).  The  beams 
should  only  be  spaced  78%  of  that  given  by  the  diagram.  Thus,  the  lo-in  Is 
should  be  7.8-in.  c.  to  c.,  the  12-in.  Is  i2.5-in.  c.  to  c.;  for  the  next  tier  the 
15-in.  Is  7.8-in.  c.  to  c.  and  the  i8-in.  Is  i2.5-in.  c.  to  c. 

(B)  Or  using  formula  (21)  the  number  of  beams  should  be  137%  of 
those  given  by  the  first  method.  That  is,  instead  of  12  and  8  beams  for  the 
first  tier,  there  should  be  16  and  n,  and  for  the  next  tier,  instead  of  5  and 
3  there  should  be  7  and  4  beams. 

SOLUTION  FOR  BUCKLING  OF  THE  WEBS. — The  tier  of  beams  directly 
under  the  base  of  the  column  always  presents  the  most  unfavorable  condi- 
tions. This  cast-iron  base  is  4  ft.  square.  By  dividing  the  load  (400  tons) 
on  the  footing  by  the  length  of  the  base,  and  the  quotient  by  the  number 
of  beams  in  the  tier,  the  load  on  each  lineal  foot  of  beam  is  obtained. 
Thus,  on  the  15-in.  beams  (considering  the  first  method  of  design),  this 
load  is  20  tons,  and  for  the  i8-in.  beams  the  load  is  33.3  tons.  By  referring 
to  the  tables  in  Chapter  VIII  it  will  be  found  that  the  allowable  load  on  the 
12-in.  beams  is  22.3  tons,  while  the  i8-in.  beams  only  carry  23.4  tons.  In 
the  latter  case  it  is  evident  that  it  would  be  impracticable  to  use  these 
three  beams. 


END   REACTIONS.  6$ 


CHAPTER  VI.— END  REACTIONS. 

The  effect  of  the  end  reaction  on  the  strength  of  a  beam  has 
been  discussed  in  Chapter  I ;  the  cause  and  effect  of  an  end  reaction 
was  referred  to  in  Chapters  III  and  IV;  while  this  chapter  briefly 
outlines  the  subject  of  end  reactions  as  considered  by  the  struc- 
tural designer  in  deciding  upon  the  relative  value  of  standard  and 
special  details  of  construction,  and  in  deciding  upon  the  design  of 
these  standard  or  special  details. 

Standard  details  materially  reduce  the  cost  of  structural  work, 
and  so  long  as  there  is  a  balance  of  saving  in  shop  work  to  pay  for 
the  excess  material  required  by  their  use,  they  should  be  adopted. 
On  the  other  hand,  the  most  liberal  standards  are  not  safe  beyond 
partially  defined  limits  and  these  limits  should  be  carefully  checked. 
It  is  hoped  this  treatment  of  the  subject  will  be  of  value  in  keeping 
a  proper  balance  between  these  conflicting  conditions. 

From  the  following  description  it  will  be  seen  that  Dia- 
gram No.  28,  gives  the  end  reaction,  due  to  uniformly  loading  a 
beam  of  any  span  so  as  to  develop  its  full  working  strength.  It  also 
gives  equivalent  values  for  area  of  a  bearing  plate  or  number  of  riv- 
ets required  for  a  pair  of  connection  angles. 

DIAGRAM  NO.  28. — This  diagram  covers  cases  of  end  re- 
actions on  beams  under  uniform  loads.  The  abscissas  represent 
span  of  beam,  ordinates  represent  end  reaction  and  diagonal  lines 
represent  the  different  sizes  of  I-beams  and  channels.  The  quanti- 
ties referred  to  are  all  found  on  the  central  part,  or  diagram  proper. 
To  the  left  and  right  will  be  found  alternative  sets  of  ordinate 
scales,  applying  directly  to  the  diagram  which  give  the  essential 
values  concerning  riveted  end  connections  and  bearing  plates. 
The  six  scales  to  the  left  of  the  diagram  show  the  number  of  J-in. 
rivets,  in  shear,  required  to  take  care  of  a  reaction  of  any  given 
amount.  Steel  and  wrought  iron  shop  rivets,  field  rivets  and  bolts 
are  represented  by  the  six  columns.  The  two  columns  at  the  right 
of  the  diagram  should  be  used  in  connection  with  these ;  they 
show  the  number  of  |-in  rivets,  in  bearing  on  a  web  i/io-in.  thick, 
required  for  any  reaction.  These  values  are  also  given  for  steel 
and  wrought  iron  rivets.  At  the  right  of  the  latter  scales  is  another 
set  of  ordinate  scales  applying  to  bearing  plates  (often  called  tem- 
plates). They  show  the  area  (in  square  inches)  of  bearing  plate 


66  STRUCTURAL    DESIGNERS*    HANDBOOK. 

required  for  any  reaction,  in  five  columns,  calculated  on  a  basis  of 
18  tons,  15  tons,  5  tons  and  8  tons  permissible  loadings  per  square 
foot.  The  usual  sizes  of  bearing  plates  are  given  in  the  last  column 
to  the  right,  at  proper  intervals  to  represent  their  area  in  square 
inches. 

To  use  the  diagram  and  auxiliary  scales  for  any  particular 
problem,  take  an  abscissa  representing  the  span  in  feet,  and  follow 
along  the  vertical  to  the  intersection  with  the  diagonal  representing 
the  size  of  I-beam  or  channel  used.  The  horizontal  at  the  inter- 
section, if  followed  to  the  reaction  scale  at  the  left  of  the  diagram, 
gives  the  actual  reaction  in  tons.  Following  the  same  horizontal 
farther  to  the  left,  the  number  of  rivets  (or  bolts)  required  in  shear 
is  found  in  the  appropriate  column.  The  same  horizontal  followed 
out  to  the  right  shows  the  number  of  rivets  required  for  bearing 
on  i/io  in.  of  web.  This  number  is  to  be  divided  by  the  actual 
thickness  in  tenths  of  an  inch  of  the  metal,  and  the  quotient  then 
represents  the  number  of  rivets  required  for  bearing. 

In  case  the  end  of  the  beam  rests  on  a  bearing  plate,  the 
horizontal  line  is  followed  out  to  the  scales  "Sizes  of  Templates," 
and  on  the  appropriate  scale  (as  described  below)  the  required  area 
in  square  inches  is  read  off. 

NOTE. — For  spans  other  than  those  given  on  the  diagrams  the  re- 
action is  given  by  the  following  rule:  For  any  given  size  of  beam,  the 
end  reaction  varies  inversely  as  the  span. 

Example. — The  end  reaction  on  a  lo-in.  25-lb.  I-beam,  lo-ft.  span,  loaded 
to  its  full  capacity,  is  6^/2  tons.  If  the  span  were  30  ft.  the  reaction  would 
be  one-third  of  &/2,  or  2.2  tons. 

The  values  to  be  obtained  from  the  diagram  just  described 
are  used  in  the  design  of  connection  angles  and  bearing  plates, 
along  with  the  following  table  and  diagram. 


DESIGN  OF  CONNECTION  ANGLES. 
STANDARD  CONNECTION  ANGLES: — The  sizes  of  angles  used 
for  "standards"  are  closely  represented  by  the  following  list : 

For  18"  Is    For  15"  Is  and  chan- 
and  over.  nels  and  under. 

Passaic,  Carnegie,  Cambria,  Jones  &  L.  4     x  4     x^        6     X4     x  H 

Pencoyd    4     x  3^  x  7Aa        6     x3^x7A« 

Am.  Bridge   4     ><4     x  Vl«        6     x4     X7A. 

Anonymous   3^  x  ?/*  x  H        3^x3y2x6A. 


END    REACTIONS.  6? 

The  lengths  of  standard  angles  for  the  several  sizes  of  beams 
are  usually  as  follows : 

For    24"  Is  i'     6"      1  g.       For   .  .10"  to  7"  Is  and  [s  o'  5"      1  g_ 

"      20"  and  18"      i'     3"  "     ..  6"  o'  3" 

15"  Is  and  [s    o'  10"  "     ..  5"  o'  2]/2"     " 

"      12"  Is  and  [s    o'     7y2"     "  "     ..  4"  and  3"  o'  2" 

The  numbers  of  shop  and  field  rivets  in  the  above  standards 
do  not  vary  very  much,  although  Pencoyd  and  the  American  Bridge 
Co.  put  in  one  extra  shop  rivet  in  the  I5~in.  and  in  the  lo-in.  to  7-in. 
standards  over  what  is  called  for  in  the  same  standards  in  the  fol- 
lowing table. 

The  strength  of  a  pair  of  connection  angles  (sometimes  called 
knees)  not  only  depends  upon  the  number  and  strength  of  the  rivets 
in  them,  but  also  upon  the  strength  of  the  metal  upon  which  the 
rivets  bear.  These  values  for  both  standard  and  special  connection 
angles  are  given  in  the  following  table. 

TABLE  GIVING  MAXIMUM  ALLOWABLE  END  REACTION 
ON  STANDARD  AND  SPECIAL  CONNECTION  ANGLES:— This 
table  (No.  16)  gives  the  maximum  load  that  can  be  safely 
carried  by  different  standard  and  special  connection  angles 
in  terms  of  the  strength  of  the  shop  and  field  rivets  in  shear 
or  bearing.  Evidently,  the  end  reaction  on  the  beam  must  not  be 
greater  than  these  values  for  shear  or  for  bearing.  The  tabular 
values  are  for  safe  shearing  capacity  (single  shear)  and  safe  bear- 
ing capacity  (for  bearing  on  1/10-in.  metal  in  web).  The  construc- 
tion of  the  table  needs  no  further  explanation.  Whenever  there 
is  reason  to  suspect  that  a  standard  connection  will  not  be  sufficient 
for  conditions  indicated  by  Diagram  No.  28,  the  capacity  of  this 
standard  should  be  found  from  the  table.  The  use  of  this  table 
is  best  illustrated  by  an  example. 

Example: — A  12-in.  31.5  Ib.  I-beam  has  lo-in.  beams  i6l/2  ft.  long  framing 
into  it  from  both  sides.  The  web  of  the  12-in.  girder  is  0.35  in.  thick,  thus 
giving  a  bearing  value  of  o.i75-in.  for  each  field  connection.  Suppose, 
wrought  iron  rivets  are  used  in  the  field,  the  permissible  end  reaction  would 
then  be  0.175  x  2.26,  or  3.95  tons.  According  to  Diagram  No.  28  this  is  the 
safe  limit  for  uniformly  loading  the  lo-in.  beams. 

In  designing  special  connection  angles  their  length  is  limited 
by  the  clear  distance  between  the  fillets  of  the  beam.  This  dis- 
tance is  given  for  all  I-beams  and  channels  in  the  tables  given  in 
Chapter  VIII. 

On  general  principles  it  is  advisable  to  use  as  large  connection 


68  STRUCTURAL    DESIGNERS'    HANDBOOK. 

angles  as  practicable,  because  they  add  stiffness  to  the  framing. 
This  is  especially  of  value  in  high  buildings. 


DESIGN  OF  BEARING  PLATES. 

The  elements  in  the  design  of  a  bearing  plate  or  template  are 
its  bearing  area  and  its  thickness. 

The  bearing  area  depends  upon  the  load  to  be  carried  (the  end 
reaction)  and  upon  the  permissible  unit  load  on  the  material  sup- 
porting the  template.  This  latter  is  specified  in  the  "Code"  (N. 
Y.  C.)  as  follows  : 

On  Brickwork: 

8  tons  per  sq.  ft.  when  lime  mortar  is  used; 
15  tons  per  sq.  ft.  when  cement  mortar  is  used; 
18  tons  per  sq.  ft.  when  Portland  cement  (i  to  3)  is  used. 
For  Rubble  Masonry: 

5  tons  per  sq.  ft.  when  lime  mortar  is  used. 

These  values  will  be  found  to  be  the  column  headings  for  tem- 
plates in  Diagram  No.  28 ;  then,  by  the  use  of  this  diagram  the  area 
of  bearing  required  is  at  once  obtained,  and  a  convenient  size  of 
template  selected. 

The  thickness  of  the  bearing  plate  depends  upon  the  material  of 
the  plate,  the  amount  of  projection  of  the  plate  beyond  the  flange 
of  the  beam  or  beams  supported,*  and  the  unit  pressure  on  the 
bottom  of  the  plate.  The  material  may  be  cast  iron,  wrought  iron 
or  steel ;  the  unit  pressure  on  the  bottom  of  the  plate  is  that  used 
in  finding  the  area  of  the  plate  (i.  e.,  5,  8,  15,  or  18  tons  per  sq.  ft., 
as  above). 

DIAGRAM  NO.  29  enables  the  required  thickness  to  be  readily 
obtained.  The  abscissas  are  amount  of  projection  in  inches.  The 
ordinates  are  thickness  of  plate,  there  being  three  different  ordinate 
scales,  for  cast  iron,  wrought  iron  and  steel,  respectively.  Differ- 
ent diagonal  lines  represent  the  different  allowable  unit  pressures 
on  the  supporting  material. 

To  use  the  diagram,  take  an  abscissa  equal  to  the  projection 
of  the  plate,  in  inches,  and  follow  up  to  the  diagonal.  The  hori- 
zontal at  the  intersection  gives,  when  followed  to  the  right,  the 
thickness  of  the  plate. 


*The  clear  distance  between  the  inside  flanges  of  a  pair  of  beams  must 
not  exceed  2.45  times  the  projection  of  the  plate  beyond  the  outside  flanges. 


END    REACTIONS. 


Table    Giving    Maximum    Allowable    E,nd    Reaction    on 

Standard   and   Special    Connection   Angles 

TABLE  16                                                                                                          All  Klvets  %»  Diam. 

Number  of 
Holes  in 
Shop  or 
Field  End  of 
Connection 
Angles. 

SHEARING 
Values  Given  for  Single  Shear 

BEARING 

Values  Given  for  TVinch 
Bearing  of  Rivets 

Steel 

Wrought  Iron 

Steel 

Wrought  Iron 

Shop 

Field 

Shop 
Rivet 

Field 

Shop 
Rivet 

Field 

Shop 
T'ns 

i-5 

Field 

Shop 

Field 

Rivet 

Bolt 

Rivet 

Bolt 

a2 

2 

Tons 

Tons 

Tons 

Tons 

Tons 

Tons 

Tons 

Tons 

Tons 

4-4 

3-5 

3-1 

3-3 

2.6 

2-4 

i-5 

I-I3 

i-J3 

"3 

4 

6.6 

7.0 

6.2 

5-o 

5-2 

4.8 

2.2 

3-° 

1.70 

2.26 

CS 

6 

II.  0 

10.5 

9-3 

8-3 

7-8 

7.2 

3'7 

4-5 

2.82 

3-39 

"5 

8 

II.  O 

14.0 

12.4 

8-3 

10.4 

9.6 

3-7 

6.0 

2.82 

4.52 

"5 

10 

II.  0 

17-5 

15-5 

8-3 

13.0 

12.0 

3-7 

7-5 

2.82 

5-65 

f6 

12 

13.2 

21.  0 

18.6 

9.9 

15.6 

14-4 

4-5 

9.0 

3-39 

6.78 

7 

H 

154 

24-5 

21.7 

"•5 

18.2 

16.8 

5-2 

10.5 

3-96 

7.91 

8 

16 

17.6 

28.0 

24.8 

13.2 

20.8 

19.2 

6.0 

12.  0 

4.52 

9.04 

9 

18 

19.8 

31-5 

27.9 

14.6 

23-4 

21.6 

6-7 

13-5 

5.08 

10.17 

10 

20 

22.  0 

35-o 

31.0 

16.5 

26.0 

24.0 

7-5 

15.0 

5-65 

11.30 

Relative    Values    of  the    Several   Sizes   of   Rivets 

Sizes  of  Kivets                     Eatio  in  Shear                  Bearing—  Ratio 

3/£»   rivet  is    to    ^"       as         I    is    to   4        or    as        3    is    to   6 

y2         "       "    "3^          "4    "     "    9        "     "         4    "     "    6 

ft         "      "    "    X          "       ii    "    "  16        "     "         5    "     "6 

7/&        "      "    ••    tf          "4    "     "    3        "     "         7    "    "   6 

i            "      "    "3^          "9    "     "    5        "     "        8    "     "    6 

i}6         "       "    "3^          "9    "     "    4         "     "         9    "     "    6 

is  for  standard  connections  for  3 ''  to    6  "  I3  and 

7    to  10 
12 

15 

18  and  20 
24 


Diagram  No.  28 

For  giving  values  for  rivet  requirements  in  connection  angles, 
also  areas  for  bearing  plates. 


(70) 


EAD    REACTIONS. 


Diagram  No*  29* 

For  giving  thickness  of  bearing  plates  of  cast  iron,  wrought 
iron  or  steel. 

PROJECTION  OF  PLATES 


4'          5"       6"      7" 


C.I. 


W.I. 


m 


f  */   S 


*/& 


Yz 


/ 


*&_ 


7"  8 


PROJECTION  OF  PLATES  , 

Note. — When  the  clear  distance  between  the  inside  flanges  of  a  pair  of 
beams  supported  by  a  single  plate  exceeds  2.45  times  the  projection  of  the 
plate  beyond  the  outside  flanges,  the  thickness  of  the  plate  is  to  be  obtained 
by  the  following  modification  of  abscissa  value  for  projection  (not  the  real 
projection).  Multiply  the  clear  inside  distance  between  flanges  by  0.41  and 
use  this  value  on  the  abscissa  scale. 


Part  ffl. — Columns  and  Truss  Members. 

CHAPTER  VIL— STEEL  COLUMNS. 

The  usual  methods  of  designing  built  steel  columns  are  either 
quite  complex  or  else  they  apply  to  specific  forms  of  section,  as 
for  instance,  to  the  so-called  zee-bar,  channel  or  plate  and  angle 
columns.  In  the  following  system  of  diagrams  and  tables,  how- 
ever, the  form  and  make  up  of  the  section  is  treated  as  a  subject 
for  secondary  rather  than  primary  consideration. 

The  radius  of  gyration  is  an  important  factor  in  the  design 
of  columns.  Numerically  the  radius  of  gyration  is  the  square  root 
of  the  quotient  obtained  by  dividing  the  moment  of  inertia  of  a 
cross  section  by  the  area  of  the  section.  This  mathematical  com- 
putation is  quite  laborious  in  the  case  of  a  built  up  section,  mainly 
because  it  has  to  be  repeated  for  every  variation  in  area  and  dis- 
tribution of  the  material  in  the  cross  section.  It  is  believed,  how- 
ever, that  such  computations  as  these  are  unnecessary.  Diagrams 
Nos.  30  and  31  give  the  radii  of  gyration  for  the  different  forms 
of  rolled  sections  and  for  the  most  common  forms  of  built  sections 
(see  explanations  later).  A  little  study  of  these  diagrams  will  con- 
vince the  designer  that  the  radius  obtained  by  this  graphical  means 
will  give  results  as  accurate  as  the  most  conservative  could  wish  to 
use  in  his  computations. 

This  radius  of  gyration,  r,  is  one  of  two  variables  that  deter- 
mine the  ratio  of  slenderness*  of  a  column.  The  other  is  the  un- 
supported length,  1,  of  the  column.  This  ratio  of  slenderness  is 

1 
expressed  by  the  quotient  of  — ,  which  is  the  factor  that  determines 

r 

the  allowable  unit  compressive  stress  to  be  obtained  from  the 
aforementioned  column  formulas  (see  Chapter  II).  However,  in 
the  treatment  of  the  subject  of  columns  herewith,  the  allowable 
unit  stress  does  not  come  directly  into  question,  because  it  has  been 
taken  into  account  in  the  construction  of  the  diagrams  for  safe 
loads. 


*See  Chapter  II. 


STEEL    COLUMNS.  73 

THREE  STEPS  ARE  TAKEN  IN  THE  DESIGN  OF  A  COLUMN  :  First, 
determination  of  the  ratio  of  slenderness ;  second,  the  area  of  the 
cross  section  is  found ;  third,  the  make  up  of  the  section  is  decided. 
These  steps  will  be  considered  in  this  order,  the  third  step  being 
taken  up  in  Chapter  VIII.  ;» 

RATIO  OF  SLENDERNESS. 

Three  diagrams  are 'given,  two  of  which  Nos.  30  and  31  are 
used  for  obtaining  the  radius  of  gyration  for  standard  sec- 
tions and  for  built  up  sections  respectively,  and  the  third — Diagram 
No.  32 — is  used  for  obtaining  the  ratio  of  the  length  of  the  col- 
umn to  the  radius  of  gyration  or  the  so-called  ratio  of  slenderness 
of  the  column. 

DIAGRAM  NO.  30: — Here  abscissas  represent  thickness  of 
metal  expressed  as  a  percentage  of  the  depth  or  diameter  of  the 
section.  Ordinates  represent  the  radius  of  gyration  in  inches.  The 
curves  represent  the  different  arrangements  of  material  as  in- 
dicated in  the  left  hand  margin. 

Thus  the  lowest  line  is  for  an  H  section  with  neutral  axis  coincident 
with  the  web,  or  for  a  star  shaped  section  (it  will  be  observed  that  the  for- 
mer has  a  depth  greater  than  the  width  of  the  flanges,  thus  corresponding 
to  the  average  I-beam  properties);  the  next  line  is  for  a  square  H  section 
with  neutral  axis  as  before;  the  next  is  for  a  solid  circular  cross  section, 
etc.  The  uppermost  curve  in  the  diagram  (that  represented  by  a  full  black 
line)  gives  the  theoretical  values  for  a  section  of  two  plates  at  a  fixed  dis- 
tance back  to  back  and  gradually  reduced  in  thickness.  In  practice  this 
section  is  very  nearly  represented  by  two  channels  or  two  I-beams  latticed 
when  the  diameter  is  taken  as  the  distance  apart  of  their  centers  of  gravity. 
Theoretically,  this  distribution  of  material  gives  the  highest  possible  radius, 
but  practically,  it  is  impossible  to  make  use  of  it  because  the  latticing  does 
not  transmit  the  stresses  due  to  eccentric  loading  satisfactorily. 

Beside  the  diagram  proper,  supplementary  abscissa  scales 
and  ordinate  scales  are  given.  Since  the  abscissas  represent  the 
thickness  of  metal  in  the  section  expressed  as  a  percentage  of  the 
diameter  or  depth  of  the  section,  different  scales  may  be  used  to 
give  the  thickness  directly  in  inches  for  different  diameters.  Such 
a  series  of  scales  is  given  in  tabular  form  above  the  diagram,  cov- 
ering diameters  from  3  ins.  to  28  ins. 

The  principal  ordinate  scale  on  the  right  hand  edge  of  the  dia- 
gram proper  gives  the  radius  of  gyration.  A  series  of  supplemen- 
tary scales  to  the  right  of  this  give  the  radius  directly  in  inches  for 


74  STRUCTURAL    DESIGNERS'    HANDBOOK. 

any  diameter  of  section.     Seven  scales  are  given,  covering  diam- 
eters from  6  ins.  to  18  ins.  inclusive. 

The  abscissa  scales  (those  in  tabular  form  above  the  diagram)  show  a 
dotted  irregular  line  which  divides  the  scales  into  two  parts.  This  line  in- 
dicates the  thickness  of  metal  which  the  "Code"  (N.  Y.  C.)  specifies  as  the 
minimum  for  the  different  diameters  of  cast  iron  columns:  Steel  column 
sections  are  as  a  general  rule  found  to  the  left  of  the  line;  at  any  rate  they 
should  for  the  sake  of  economy  fall  to  the  left  of  the  line,  since  otherwise 
the  metal  is  needlessly  thick  and  may  be  better  utilized  by  making  the  sec- 
tion larger  and  using  thinner  metal. 

The  values  in  this  diagram  are  entirely  independent  of  the 
material  of  the  column,  and  the  sections  shown  cover  the  common 
forms  of  cast  iron  and  wooden  columns  as  well  as  the  built-up  sec- 
tions of  steel  columns.  It  should  be  remembered  that  for  all  ma- 
terials a  similar  distribution  gives  similar  values  for  the  radius  of 
gyration. 

To  use  Diagram  No.  30,  after  the  general  style  of  the  section 
of  the  column  has  been  decided  upon,  take  an  abscissa  representing 
the  thickness  of  metal  (either  as  a  percentage  of  the  diameter  on  the 
lower  scale,  or  in  inches  on  the  proper  scale  above  the  diagram) 
and  follow  the  vertical  up  to  the  curve  which  represents  the  style 
of  section  selected.  The  horizontal  at  the  intersection  gives  the 
radius  of  gyration  on  one  of  the  ordinate  scales  at  the  right  of  the 
diagram. 

DIAGRAM  NO.  31  is  for  the  same  purpose  as  the  preceding 
except  that  the  sections  are  for  the  most  common  built-up  steel 
columns.  Its  construction  is  similar  to  that  of,  the  preceding  dia- 
gram: Curves  are  drawn  for  different  sections,  and  the  ordinates 
to  these  curves  give  the  radius, of  gyration  in  inches ;  a  series  of  or- 
dinate scales  is  provided  at  the  right  for  different  values  of  the  diam- 
eter (depth)  of  the  section,  and  the  radius  of  gyration  is  read  off 
on  the  appropriate  scale.  The  left  hand  end  of  the  curves  denotes 
the  minimum  thickness  of  metal  ordinarily  used  in  practice  for  any 
one  of  the  sections  represented  by  a  curve,  while  the  right  hand 
end  corresponds  to  the  usual  maximum  thickness  employed  for 
that  type  of  section.  The  curves  then  show  the  variation  of  the 
radius  of  gyration  as  the  thickness  of  metal  used  increases  from  the 
least  to  the  greatest  thickness  ordinarily  used.  t 

NOTE:— Attention  is  drawn  to  the  fact  that  in  the  outline  sketches  for 
the  different  sections  represented  by  curves  on  this  diagram,  dimension  ar- 
rows are  shown  which  indicate  the  particular  dimension  taken  to  be  the 


STEEL    COLUMNS.  75 

"diameter."    Thus,  in  the  case  of  the  Z-bar  column,  the  width  of  the  web 
plate  is  the  diameter  for  the  neutral  axis  perpendicular  to  the  web. 

The  use  of  Diagram  No.  31  will  be  quite  clear  from  the  pre- 
ceding. It  presupposes  a  selection  of  the  type  of  section  to  be 
used  in  the  particular  case,  and  further  the  ability  to  judge  approx- 
imately what  relative  thickness  of  metal  will  be  required  with  that 
section  to  carry  the  load. 

DIAGRAM  NO.  32: — The  ratio  of  slenderness  of  a  column  is 
graphically  represented  on  this  diagram.  Abscissas  represent 
length  in  feet  and  ordinates  represent  the  ratio  of  slenderness. 
Curves  drawn  on  the  diagram  represent  various  values  of  the  ra- 
dius of  gyration  in  inches. 

It  is  to  be  noted  that  while  for  convenience  the  abscissa  scale  shows 
length  in  feet  and  the  radius  of  gyration  in  inches  the  ratio  of  slenderness — 
or  quotient  of  the  two — is  given  as  if  both  were  in  inches. 

To  use  the  diagram  for  any  particular  problem,  take  an  ab- 
scissa equal  to  the  length  of  the  column  in  feet  and  follow  the  ver- 
tical up  to  the  curve  representing  the  radius  of  gyration  of  the 
column  section  selected.  The  horizontal  at  the  intersection  shows 
on  the  ordinate  scale  the  desired  quotient,  i.  e.,  the  ratio  of  the 
length  to  the  radius  of  gyration. 

SECTION  AREAS. 

As  previously  stated  the  second  set  of  diagrams  give  the  areas 
of  cross  sections  of  columns  for  known  loads  and  known  values  for 
the  ratio  of  slenderness.  These  areas  may  conveniently  be  divided 
into  three  classes ;  area  necessary  for  concentric  load  when  ends 
of  columns  are  "flat" ;  area  or  areas  necessary  for  eccentric  load 
when  ends  are  flat  and  securely  braced  laterally  in  the  direction 
or  directions  of  the  eccentricity ;  and,  area  necessary  when  pin 
ends  are  used.  Values  for  these  three  classes  of  loading  are  given 
on  Diagrams  Nos.  33  and  34 — Diagram  No.  33  which  gives  the 
area  required  for  concentric  loading  on  a  column  with  flat  ends 
facing  the  principal  diagram  of  this  group,  because  the  two  latter 
values  are  given  in  per  cent,  of  the  first.  This  is  more  fully  ex- 
plained below  under  the  separate  heads. 

SECTION  AREAS  FOR  CONCENTRIC  10 ADING :— Diagram 
No.  33  gives  the  safe  load  on  medium  steel  columns  for  any  ratio 
of  slenderness  and  any  area  of  cross  section.  In  this  diagram, 


76  STRUCTURAL    DESIGNERS'    HANDBOOK. 

abscissas  represent  values  for  any  ratio  of  slenderness  from  10  t> 
200 ;  ordinates  represent  the  area  of  cross  section  in  square  inches ; 
curves  on  the  diagram  represent  different  values  for  the  safe  load 
capacity  of  the  column. 

Several  supplementary  scales  appear  on  the  diagram.  At  the 
bottom,  just  above  the  main  abscissa  scale,  is  a  scale  showing 
"Rate  of  increase  of  area"  for  any  given  load  and  length  of  column 
with  varying  ratio  of  slenderness. 

This  scale  will  be  found  valuable  in  indicating  the  effect  of  changes  in 
dimensions  of  cross  sections  upon  the  amount  of  metal  required  in  a  col- 
umn. Thus  it  shows  the  importance  of  keeping  the  ratio  of  slenderness 
down  as  low  as  possible.  For  instance,  a  ratio  of  170  calls  for  three  times 
as  much  material  as  a  ratio  of  10. 

At  the  extreme  right  of  the  diagram  is  a  scale  of  weights ;  it 
shows  the  weight  of  the  column  per  lineal  foot  for  any  area  of  cross 
section  in  square  inches. 

A  further  supplementary  abscissa  scale  on  the  lower  part  of  the 
diagram  gives  the  area  for  pin  end  columns  in  the  form  of  percent- 
age factors,  based  on  the  section  area  required  for  an  equivalent 
load  on  a  column  with  flat  ends  i.  e.  as  found  on  the  main  part  of 
the  diagram. 

SECTION  AREAS  FOR  CONCENTRICALLY  LOADED  COL- 
UMNS WITH  PIN  ENDS:— When  the  ends  of  a  column  are  hinged 
or  have  pin  bearings  it  is  less  rigid  than  when  the  ends  are  flat.  For 
this  reason  lower  unit  stresses  are  allowed  for  pin  end  columns. 
The  "Code"  (N.  Y.  C.)  makes  an  equivalent  provision  by  saying 
"the  working  stress  in  struts  of  pin  connected  trusses  shall  not  ex- 
ceed 75%  of  the  working  stresses  for  flat  ends."  This  gives  a  flat 
increase  of  33V3%  in  tne  area  of  tne  section  for  all  column  ratios. 

The  percentages  given  by  the  aforementioned  supplementary 
scale  show  values  increasing  as  the  column  ratio  increases.  Thus,, 
for  a  column  ration  of  100  the  percentage  is  120,  i.  e.,  the  pin  end 
column  should  be  given  one-fifth  more  section  area  than  a  flat-end 
column  with  the  same  ratio  of  slenderness  and  with  the  same  load ;. 
for  a  column  ratio  of  150  the  percentage  is  nearly  155. 

SECTION  AREAS  FOR  TENSION  MEMBERS:— The  scale  on 
Diagram  No.  33  to  the  left  of  the  scale  of  weights,  on  the  right 
hand  edge  of  the  diagram,  gives  values  for  loads  in  tension  for  dif- 
ferent areas  of  section  (or  weights  per  lineal  foot),  based  on  a  ten- 
sile strength  of  16,000  Ibs.  per  sq.  in.  of  net  section. 


STEEL   COLUMNS.  77 

NOTE: — This  latter  scale  has  absolutely  no  bearing  on  the  use  of  this 
.diagram  for  the  design  of  columns.  It  is  intended  for  use  in  the  design  of 
trusses  where  both  compression  and  tension  members  occur  together  and 
will  be  very  useful  for  such  work.  The  tables  of  properties  of  shapes  in 
Chapter  VIII,  are  convenient  for  use  with  this  scale  as  well  as  for  use  with 
the  diagram  proper. 

THE  USE  OF  DIAGRAM  NO.  33  will  be  evident  from  the  pre- 
ceding. Taking  an  abscissa  equal  to  the  ratio  of  slenderness  of 
the  column,  the  intersection  of  the  vertical  with  the  curve  represent- 
ing the  load  gives  the  required  area  of  section  on  the  ordinate  scale 
to  the  left,  or,  the  required  weight  per  lineal  foot  on  the  ordinate 
scale  to  the  extreme  right.  If  the  column  has  pin  ends  this  area  (or 
weight)  must  be  multiplied  by  the  percentage  factor  found  on  the 
scale  above  the  column  ratio.  The  other  scales  are  used  in  ac- 
cordance with  the  foregoing  descriptions. 

It  is  generally  not  advisable  to  employ  columns  with  a  higher  ratio  of 
slenderness  than  120.  The  "Code"  (N.  Y.  C.)  limits  important  columns  to 
this  ratio  as  a  maximum,  and  the  allowed  stresses  for  columns  are  given 
only  for  ratios  of  120  and  less.  As  it  was  considered  advisable  to  extend  the 
use  of  Diagram  No.  33  beyond  this  point  so  as  to  include  ratios  up  to  200 
the  following  method  was  used  to  supply  safe  values  for  allowable  unit  stress 
in  case  of  ratios  between  120  and  200.  Different  well  established  column 
formulas  were  plotted  and  the  curve  representing  the  unit  stresses  allowed 
by  the  "Code"  was  extended  parallel  to  the  direction  of  the  mean  of  the 
other  curves.  The  resulting  curve  was  used  to  get  safe  allowable  unit 
stresses  for  ratios  beyond  120. 

SECTION  AREAS  FOR  ECCENTRIC  LOADING:— It  will  be  re- 
membered that  Chapter  II  contains  discussions  on  the  strength  of 
columns  under  concentric  and  eccentric  loading.  The  term  z  y — 
there  defined  as  the  coefficient  of  eccentricity — when  divided  by  the 
square  of  the  radius  of  gyration  about  the  axis  for  which  the  load 
is  eccentric  gives  a  percentage  factor  for  the  area  necessary  to  take 
care  of  the  bending  moment  due  to  this  eccentricity. 

NOTE: — A  little  care  in  the  arrangement  of  beams  and  girders  will  of- 
ten eliminate  the  eccentricity  of  loading  on  columns.  There  are,  however, 
many  cases  where  it  cannot  be  avoided.  For  such  cases  the  "Code"  (N.  Y. 
C.)  provides  that: 

Any  column  eccentrically  loaded  shall  have  the  stresses  caused  by  such 
eccentricity  computed,  and  the  combined  stresses  resulting  from  such  eccen- 
tricity at  any  part  of  the  column,  added  to  all  other  stresses  at  that  part 
shall  in  no  case  exceed  the  working  stresses  stated  in  the  "Code."  The  ec- 
centric load  of  a  column  shall  be  considered  to  be  distributed  equally  over 
the  entire  area  of  that  column  at  the  next  point  below  at  which  the  column 
is  securely  braced  laterally  in  the  direction  of  the  eccentricity. 


?  STRUCTURAL    DESIGNERS'    HANDBOOK. 

It  will  be  apparent  that  these  provisions  have  been  adhered  to 
in  the  treatment  of  eccentric  loads  herewith  presented. 

DIAGRAM  NO.  34  gives  the  aforementioned  percentage  of 
area  necessary  to  take  care  of  eccentricity  of  loading.  In  this  dia- 
gram abscissas  represent  the  radius  of  gyration,  while  ordinates 
represent  coefficient  of  eccentricity.  Curves  on  the  diagram  rep- 
resent the  percentage  of  area  to  be  added  to  a  cross  section  for  the 
eccentricity  of  the  loading  on  the  column.  An  example  will  best  il- 
lustrate the  use  of  Diagrams  Nos.  33  and  34. 

Example: — A  column  10  ft.  long  has  a  load  of  140  tons,  15  tons  of  which 
is  located  5  ins.  from  each  neutral  axis.  The  column  section  is  built  up  with 
plates  and  angles  in  the  form  of  an  H.  The  assumed  dimension  back  to  back 
of  angles  is  10  ins.,  and  8  ins.  is  the  dimension  the  other  way. 

Solution: — The  center  of  gravity  of  the  combined  concentric  and  ec- 
centric load  is  located  0.535  in.  from  both  principal  axis.  The  coefficient  of 
eccentricity  in  the  direction  parallel  to  the  web  is  0.535  times  5  or  2.68;  in 
the  direction  perpendicular  to  the  web  it  is  0.535  times  4  or  2.14.  For  the 
direction  parallel  to  the  web  in  which  case  the  radius  is  4  ins.,  the  diagram 
No.  33  gives  the  area  of  metal  required  for  this  eccentricity  as  17%  of  what 
would  be  required  for  the  same  load  concentrically  located.  For  the  direc- 
tion perpendicular  to  the  web  in  which  case  the  radius  is  2  ins.,  it  is  53% 
of  that  same  area.  The  sum  of  these  three  areas  which  go  to  make  up  the 
material  of  the  cross  section  can  be  found  in  two  ways  from  these  diagrams. 

First: — The  area  required  for  a  concentric  load  of  140  tons  may  be 
found  on  Diagram  No.  33  and  the  foregoing  70%  (17  +  53)  can  then  be  added 
to  it,  giving  the  total  area  of  cross  section. 

Second: — The  load  may  be  increased  to  what  would  be  an  equivalent 
concentric  load— 170%  of  140  or  238  tons.  Evidently  the  area  may  then  be 
found  directly  on  Diagram  No.  33.  This  same  diagram  also  gives  the  equiv- 
alent weight  per  lineal  foot  of  the  section.  For  a  concentric  load  of  140 
tons  and  a  ratio  of  slenderness  of  60  this  weight  is  81.5  Ibs.  and  for  a  load  of 
238  tons,  the  weight  of  the  cross  section  is  about  139  Ibs. 

According  to  this  diagram  139  Ibs.  per  lin.  ft.  represents  41  sq.  ins.  of 
cross  section.  This  would  require  approximately  1^4  in.  thickness  of  metal 
for  the  assumed  dimensions  of  the  section,  thus,  it  would  be  advisable  to  in- 
crease the  dimensions  until  the  thickness  is  much  reduced. 

The  areas  and  weights,  of  structural  shapes  used  for  column 
sections,  are  given  in  the  next  chapter. 


STEEL    COLUMNS. 


79 


Example.— The   radius  of  gyration  of  a   round  column   about  %- 
metal  is  3.25  for  10  ins.  diameter. 


inch 


So 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


Diagram  No.  3J 

For  giving  the  radius  of  gyration  of  the  most  common  forms 
of  built-up  column  sections. 


DIAMETER  OF  SECTION  IN  INCHES 
6       7       8      9     10     11     12     13     14     15 


STEEL    COLUMNS. 


81 


Diagram  No.  32 

For  giving  the  ratio  of  slenderness  of  a  column. 
UNSUPPORTED  LENGTH   IN  FEET 


co 

UJ 

cc. 

UJ 
Q 

UJ 
_J 

co 

u_ 
O 

O 

i 


UNSUPPORTED   LENGTH   IN   FEET 

Example. — A  column  12  ft.  long  with  a  radius  of  gyration  of  2.6 
ratio  of  slenderness  of  55. 


has  a 


Diagram  No.  33 

For  giving  the  safe  loads  on  steel  columns  as  called  for  by  the 
New  York  Building  Code  for  ratios  of  slenderness  up  to  120,  and 
as  recommended  by  the  author  for  ratios  between  120  and  200. 


RATIO  OF  SLENDERNESS 

Example. — A  column  having  a  ratio  of  slenderness  of  70  and  a  load  of 
54  tons  requires  9.8  sq.  ins.  in  its  cross-section  (or  33.3  Ibs.  per  lin.  foot). 

(82) 


STEEL    COLUMNS.  83 

Diagram  No*  34 

For  Eccentric  Loading  on  Columns. 

This  diagram  gives  the  percentage  of  material  necessary  to 
add  to  the  cross-section  of  a  column  for  any  eccentricity  of  the 
centre  of  gravity  of  its  load  with  reference  to  the  axial  planes 
through  its  neutral  axis. 

RADIUS  OF  GYRATION   IN   INCHES 


RADIUS  OF  GYRATION   IN   INCHES 

Note. — The  material  in  a  column-section  with  two  principal  axes  of  sym- 
metry—as in  Figs.  3  to  23 — may  be  said  to  perform  three  functions  when 
the  load  on  the  column  is  eccentric:  Part  cares  for  the  load  as  purely 
concentric,  another  part  cares  for  the  load  as  eccentric  on  the  axis  where 
the  radius  of  gyration  is  a  minimum,  and  the  remainder  on  the  axis  where 
the  radius  is  a  maximum. 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


CHAPTER  VIII.     TABLES. 

PROPERTIES  OF  SINGLE  AND  BUILT-UP  STEEL 
SHAPES  OF  I-BEAMS,  CHANNELS,  ANGLES,  TEES, 
ZEES,  AND  FLATS  FOR  USE  IN  COLUMNS,  BEAMS 
AND  TRUSSES. 

EXPLANATIONS:— The  tables  of  properties  in  this  chapter 
while  intended  to  cover  the  whole  range  of  needs  in  structural  de- 
sign, are  grouped  with  the  treatment  of  column  design  for  two 
reasons;  first,  the  subject  of  beam  design  is  so  thoroughly  covered 
t>y  independent  diagram  treatment,  that  only  occasional  use  will  be 
made  of  beam  properties;  second,  the  subject  of  column  design, 
being  impossible  of  independent  diagram  treatment  because  of  the 
complex  forms  of  built  sections,  makes  necessary  a  combination  of 
diagrams  and  tables.  In  the  first  case  the  use  of  independent  dia- 
grams was  made  possible  by  the  simplicity  of  form  of  the  standard 
section,  the  I-beam  (occasional  use  of  channels,  angles  and  tees 
•excepted),  being  used  almost  exclusively.  On  the  other  hand,  col- 
umns have  only  to  a  very  small  extent  become  standardized  as  re- 
gards section ;  practically  all  steel  columns  are  built  sections,  i  e. 
are  built  up  of  elementary  structural  shapes,  and  their  proportions 
and  sizes  vary  widely.  This  is  one  of  the  conditions  that  compli- 
cates column  design  and  makes  it  impossible  of  independent  dia- 
gram treatment. 

The  properties  of  the  standard  sections  given  in  the  tables  are 
for  the  single  shapes,  for  a  pair  of  shapes,  and  also,  in  the  case  of 
angles  and  zees,  for  four  shapes  combined.  In  the  latter  case  as 
well  as  in  the  cases  of  pairs  of  I-beams  or  pairs  of  channels  these 
combined  shapes  are  supposed  to  be  latticed*  together. 

The  aforementioned  standard  sections,f  adopted  by  the  Amer- 
ican Association  of  Steel  Manufacturers,  as  represented  by  Car- 
negie, Cambria,  Jones  and  Laughlins  and  Phoenix  are  given  in 
these  tables;  also  distinctive  and  well  marked  differences  in  the 
Passaic  and  Pencoyd  standards  have  been  taken  into  account. 

'  *When  plates  are  used  instead  of  lattice  bars,  the  radius  of  gyration 
should  be  taken  from  the  diagrams  in  the  preceding  chapter  and  not  from 
these  tables,  except  when  special  tables  are  appended  with  these  values  which 
is  the  case  for  channel  and  zee-bar  columns.  These  give  correct  values  for 
radius  of  gyration  about  both  axes  for  cover  and  web  plates  respectively. 
fSee  note  in  Chapter  III. 


TABLES.  85 

NOTE: — The  first  mentioned  group  of  rolling  mills  do  not  in  every  case 
roll  the  full  list  given  in  the  tables,  but  differences  of  this  kind  have  not  been 
noted. 

DIMENSIONS  AND  WEIGHTS:— The  dimensions  and  weights 
per  lineal  foot  given  for  all  the  sections  in  the  tables  are  fully  ex- 
plained under  their  respective  heads.  However,  it  should  be  men- 
tioned that  the  ''Practical  Detailing  Dimensions"  given  in  most  of 
these  Tables  are  not  to  be  considered  as  arbitrary  values— they 
represent  mean  values.  The  gage  given  for  the  I-beam  is  the  dis- 
tance between  the  two  lines  of  rivets  on  the  flanges.  Thus,  the  dis- 
tance from  the  center  line  of  the  web  to  the  rivet  line  in  the  flange 
on  either  side  is  equal  to  one-half  of  the  gage  given  in  the  table. 
The  gage  for  channels  is  given  from  their  back.  Gages  for  a  sin- 
gle and  double  line  of  rivets  on  the  legs  of  angles  are  given  in  the 
table  of  angles  with  even  legs.  The  first  dimension  in  each  case  is 
given  for  the  gage  of  a  single  line  of  rivets  and  directly  below  it  is 
given  the  gages  for  a  double  line  of  rivets  for  the  same  leg. 

As  stated  in  the  foregoing  the  range  of  application  of  these 
tables  includes :  beams  and  columns  used  in  buildings ;  tension  and 
compression  members  used  in  trusses ;  and  flanges  used  in  plate 
girders.  These  several  uses  will  now  be  considered  under  their 
separate  heads. 

BEAMS. 

The  more  generally  used  beam  property  is  the  section-mo- 
ment. It  is  given  in  all  of  the  following  tables  for  the  two  principle 
axes  of  each  section  in  foot-pounds  for  angles  and  tees  and  foot- 
tons  for  all  other  shapes.  This  is  the  safe  resisting  property  of  a 
beam  which  opposes  the  bending  moment  of  the  external  forces 
acting  upon  it ;  and  the  Formulas  Nos.  I  to  14,  given  in  Chapter  I 
arc  for  the  purpose  of  illustrating  the  application  of  this  section- 
moment  in  the  design  of  beams  or  girders. 

The  allowable  values  for  the  web  of  I-beams  in  compression 
and  for  the  end  reactions  on  beams  have  been  fully  described  in 
Chapters  I  and  V  and  the  use  of  these  values  will  be  readily  un- 
derstood without  further  explanations. 

WHEN  IT  is  DESIRED  TO  USE  PLATES  ON  THE  TOP  AND 
BOTTOM  FLANGES  OF  AN  I-BEAM  or  a  pair  of  I-beams,  or  on  the 
top  and  bottom  flanges  of  a  pair  of  channels,  the  following  method 
may  be  employed  to  determine  the  area  of  the  plates : 

From  the  external  bending  moment  deduct  75%  of  the  section-moment 


86  STRUCTURAL    DESIGNERS'    HANDBOOK, 

of  the  beam  or  beams  (given  in  the  tables)  and  divide  this  by  the  product 
of  the  depth  (c.  to  c.  of  plates  in  feet)  and  7.2.  (Formula — 22) 

This  quotient  gives  the  net  area  of  the  plates  on  each  flange. 
Diagram  No.  33  may  be  used  to  find  an  equivalent  weight  per  lineal 
foot  for  such  an  area  of  metal  and  Table  No.  25  will  give  the 
several  possible  dimensions  for  the  width  and  thickness  of  these 
plates. 

TRUSSES  AND  PLATE  GIRDERS. 

The  theory  and  practice  of  the  design  of  trusses  and  plate 
girders  (including  the  subject  of  rivet  spacing)  is  beyond  the  scope 
of  the  present  book  and  in  the  following  a  general  knowledge  of 
the  subject,  on  the  part  of  the  reader,  is  assumed. 

IN  THE  DESIGN  OF  TRUSSES,  pure  compression  and  pure 
tension  usually  prevail  in  both  the  web  and  chord  members.  How- 
ever, when  loads  occur  on  the  top  and  bottom  chords,  flexure 
stresses  are  thereby  added  to  these  direct  stresses.  For  the  design 
of  members  in  pure  tension  and  pure  compression,  no  further  ex- 
planations will  be  required  than  have  already  been  given ;  while 
for  cases  of  combined  stresses  of  flexure  and  tension  or  flexure  and 
compression  the  diagram  for  eccentric  loading  may  be  utilized  in 
a  very  simple  manner : — 

For  instance,  the  eccentric  load  P  (see  Fig.  i)  considered  in  the 
subject  of  column  design  now  becomes  a  transverse  instead  of  an 
axial  load  on  the  truss  member,  and  this  transverse  load  produces 
a  similar  bending  moment  on  the  member.  This  bending  moment 
due  to  transverse  loading  is  found  by  introducing  a  new  value  for  s, 
which  is  obtained  as  follows :  Suppose,  a  and  b  are  the  respective 
distances  of  the  load  from  the  two  ends  of  the  member,  then,  z 
ab 

equals for  any  position  of  the  load  on  the  truss  member. 

a  +  b 

Therefore,  the  percentage  of  area  of  the  cross  section  necessary 
to  take  care  of  the  flexure  stress  (either  tension  or  compression) 
can  be  found  by  the  use  of  Diagram  No.  34,  after  having  determined 
upon  the  value  of  the  radius  of  gyration  of  the  proposed  section, 
either  from  the  following  tables  or  from  Diagram  Nos.  30  or  31. 

ab 

The  coefficient  of  eccentricity  being y  instead  of  z  y   as  in 

a  +  b 


TABLES.  87 

the  case  of  columns  where  y  is  the  distance  from  the  neutral  axis 


p 


to  the  extreme  fiber,  as  before.    Thus  A  = 


(23). 


When  the  load  P  is  in  the  middle  of  the  beam  and  both  ends  are 
fixed,  the  area  will  be  one-half  that  given  by  the  above  formula. 
The  use  of  the  diagrams  and  tables  for  tension  and  compres- 
sion members  has  already  been  described  in  the  preceding  chapter 
on  steel  column  design. 

NOTE: — Deductions  for  rivet  holes  in  tension  'members  may  be  made 
as  follows:  The  area  of  metal  required  for  a  fy-in.  rivet  is  0.88  sq.  ins.  for 
every  inch  thickness  of  metal — this  is  equivalent  to  a  reduction. of  3  Ibs,  pec 
lin.  ft.  in  the  weight  of  the  section.  Thus,  if  the  metal  is  ^2  in.  thick,  iV?  Ibs. 
per  lin.  ft.  should  be  added  to  the  net  section.  Accurate  values  for  various 
thicknesses  of  metal  from  l/\,  in.  to  2  ins.  are  given  in  Table  No.  25  for 
l/2  in.  and  ^  in-  rivets. 

PLATE  GIRDERS:— A  general  discussion  of  the  subject  of 
plate  girder  design  is  beyond  the  scope  of  this  book.  The  tables 
given  herewith,  however,  lend  themselves  readily  to  the  design  of 
an  important  element  of  plate  girders — the  flanges. 

The  area  of  the  flange  is  found  by  the  use  of  the  following 
formula  when  the  value  of  the  section-moment  in  the  web  is 
neglected : — 

Mb 

Fa  =  0.143 (24a) 

*  .•  '  h 

where 

Fa   =  the  net  area  of  the  tension  flange  in  square  inches, 
Mb  =  the  external  bending  moment  in  foot-tons, 
and  h       =  the  distance,  in  feet,  between  centers  of  gravity  of  flanges. 

Now,  as  the  weight  per  lineal  foot  of  pairs  of  angles  is  given  in 
the  tables  in  preference  to  the  area  of  the  sections,  this  formula 
becomes 

Mb 

Fw  -  0.485  ,  (24) 

h 
where 

Fw  =  the  weight  in  pounds  per  lineal  foot  of  the  tension  flange,  and  the 
other  values  same  as  foregoing. 

It  is  customary  to  make  the  compression  flange  of  a  plate 
girder  the  same  as  the  tension  flange. 


88  STRUCTURAL    DESIGNERS'    HANDBOOK. 

COLUMNS  MADE  OF  BUILT  STEEL  SHAPES. 

In  Figs.  3  to  18  herewith,  are  exhibited  a  number  of  built  steel 
column  sections.  They  do  not  represent  every  possible  variation 
in  arrangement  of  material ;  as  a  matter  of  fact  it  is  not  desirable  to 
more  than  indicate  the  general  methods  of  distributing  the  mate- 
rial in  a  cross  section,  because  the  system  presented  in  this  book 


Pig.  3. 


Fig.  4. 


HH 

Fig.  e. 


Fig.  6. 


for  the  design  of  columns  admits  of  any  arrangement  or  distribu- 
tion of  the  material  that  the  ingenuity  of  the  designer  may  dictate. 
This  fact  will  be  better  understood  from  a  description  of  the  various 
types  of  column  sections*  : — • 

COMBINATIONS  WITH  I-BEAMS  : — Figs.  3  to  6  refer  to  the  use  of 
an  I-beam  to  combine  channels,  I-beams  or  plates,  etc.  For  a 
single  I-beam,  and  a  pair  of  latticed  I-beams,  the  tables  given  in 
this  chapter  are  complete.  When  an  I-beam  is  used  to  connect  a 
pair  of  I-beams  or  a  pair  of  channels,  as  in  Figs.  5  and  6,  special 
tables  may  be  easily  made  by  the  designer.  The  only  values  re- 
quired in  these  special  tables  being  the  sum  of  the  weights  of  the 
combined  sections,  and  the  dimensions  with  which  to  determine 
the  radii  of  gyration  from  Diagrams  Nos.  30  and  31. 

CHANNEL  COLUMNS  : — This  type  of  column,  Figs.  7,  8,  and  9, 


aaax...... 

Mb         ^j 

Fig.  7. 


Fig.  8. 


Fig.  0. 


is  the  most  popular  of  the  closed  sections.  For  this  reason  a 
special  table  has  been  appended  to  the  general  table  of  properties 
of  channels.  The  properties  of  a  pair  of  latticed  channels  are  given 
in  the  general  table.  When  plates  are  added  to  the  webs  of  the 
channels  as  in  Fig.  9  special  tables  may  be  made. 

*No  attempt  is  made  to  enter  into  a  discussion  of  the  relative  merits  of 
column  sections.  This  aspect  of  the  subject  is  taken  up  in  books  like  Frie- 
tag's  "Architectural  Engineering"  and  books  by  Birkmire. 


TABLES. 


89 


PLATE  AND  ANGLE  COLUMNS: — Figs.  10  to  16  illustrate  in  a 
small  way  the  various  combinations  that  may  be  made  by  the  use 
of  angles  and  plates.  The  type  of  column  indicated  by  Figs.  10 
and  ii  is  most  popular  with  advocates  of  open  sections.  For  this 
reason  a  special  table  is  also  appended  to  the  tables  of  properties 

ixwn 


Fig.  10. 


Fig.  11. 


Fig.  12. 


Fig.  13. 


Fig.  14.        Fig.  15. 


Fig.  16. 


of  angles.     Evidently  other  special  tables  can  be  made  to  cover 
an  endless  variety  of  combinations  of  these  two  sections. 

ZEE-BAR  COLUMNS: — Figs.  17  and  18  illustrate  two  of  the 
more  common  forms  of  this  type  of  column.  Table  No.  24  though 
small  gives  quite  a  variety  of  information  on  these  column  sections. 
For  instance :  Two  methods  of  design  are  considered,  one  giving 
weight  of  section  for  varying  widths  of  web  and  the  other  for  a 
constant  width  of  web.  This  latter  is  a  favorite  idea  with  some 
designers,  giving  as  it  does,  one  important  constant  dimension  for 


H 


Fig.  17.  Fig.  18. 


the  column.    Other  special  tables  can  also  be  made  for  any  other 
desired  arrangement  of  material. 

MISCELLANEOUS  SECTIONS: — The  several  tables  on  I-beams, 
channels,  tees,  and  angles  may  evidently  be  used  for  the  application 
of  any  single  shape  to  strut  design. 


STEEL   I=BEAMS 

For  Beams,  Girders,  Columns,  or  Truss  Members           TABLE  17 

• 

2 

3 

4 

5 

6              7 

8 

I 

Weight 
Per  Foot 

Dimensions 

1  1 

"§® 

Neutral  Axis 
Perpendicular  to 
Web 

•i 
i 

I 

"o 

3 

a<a 

00 

ii 

II 

1 
|| 

IW    © 

II    I! 

— 

0 

If 

ojs 

EM  ® 

c*fe 

©«-c 

SB            "t  § 

fc 

1 

w 

PN 

PQ 

* 

1 

3° 

is     &2 

I 

[nches 

Lbs. 

Lbs. 

Inches 

Inches 

Square 
Inches 

Inches 

Foot- 
Tons 

i 

ac 

3 

5-5 

il 

2.33 

0.17 

1.62 

.2 

I.I 

2 

ac 

6.5 

13 

2.42 

0.26 

1.91 

.2 

1.2 

3 

ac 

7-5 

15 

2.52 

0.36 

2.20 

.1 

i-3 

4 

b 

4 

6.0 

12 

2.19 

0.18 

I.76 

.6 

1.5 

5 

d 

7-5 

15 

2.66 

0.19 

2.20               .6 

2.0 

6 

ac 

8.5 

17 

2-73 

0.26 

2.50             .6 

2.1 

7 

ac 

9-5 

19 

2.81 

0-34 

2.79 

•  5 

2.2 

8 

b 

10 

2O 

2.69 

0-39 

2  94 

•  5 

2-3 

9     j     ac 

10.5 

21 

2.88 

0.41 

3-09 

•5 

2.4 

10 

d 

5 

9-75 

19-5 

3.00 

0.21 

2.87 

2.1 

3.2 

ii 

b 

12 

24 

3-13 

0.34 

3-53 

2.0 

3-6 

12 

ac 

12.25 

24-5 

0.36 

3.60 

1.9 

3-6 

J3 

b 

13 

26 

3  13 

0.26 

3-82 

2.1 

4.2 

14 

ac 

14-75 

29.5 

3-29 

0.50 

4-34 

1.9 

4.0 

15 

b 

15 

3° 

3-25 

0-38 

4.41 

2.0 

4-5 

16 
i7 

b 
ac 

6 

12 
12.25 

24 
24-5 

3.38 
3.33 

O.22 
0.23 

3-53 
3.60 

2-5 

2.5 

4.8 
4.8 

18 

ac 

14.75 

29-5 

3-45 

o-35 

4-34 

2.4 

5-3 

19 

b 

15 

30 

3-52 

0.25 

4.41 

2-5 

5-9 

20 

ac 

I7.25 

34-5 

3-57 

0.48 

5-07 

2-3 

5-8 

21 

b 

17.5  ' 

35 

3-64 

0-37 

5-14 

2.4 

6.4 

22 

b 

2O 

40 

3-77 

0.50 

5.88 

2.3 

6.9 

23 

c 

32.3 

4-88 

0.50 

•  9  49 

2.3 

11.5 

24 

c 

37-4 

10.99 

2.3 

12.5 

25 

c 

41 

5-25 

0.63 

12.65 

2.3 

14.2 

26 

c 

46.1 

13-55 

2.3 

IS-2 

27 

d 

7 

15 

30 

3.66 

0.25 

4.41 

2.9 

69 

28 

d 

17-5 

35 

3-76 

o-35 

5-i4 

2.8 

7-5 

29 

d 

20 

40 

3-87 

0.46 

5.88 

2.7 

8.0 

30 

b 

22 

44 

4.17 

0.36 

6.47 

2.8 

9-5 

31 

d 

8 

18 

36 

4.00         0.27 

5-29 

3.3 

9.5 

32 

b 

20 

40 

4.20          0.32 

5.88 

32 

IO.O 

33 

ac 

20.5 

4.08          0.36 

6.  02 

3-2 

10  I 

34 

d 

22 

44 

4.38          0.29 

6-47          3-3 

ii.  6 

35 

ac 

23 

46           4.18 

0-45 

6.76          3.1 

10.7 

36 

b 

25 

50 

4.49 

0.40 

7-35           3-2 

12.4 

37 

ac 

25-5 

427 

0.5+ 

7-49     !      3-° 

11.4 

38 

b 

27 

54 

4-56 

0.48 

7-93           3-i 

12.9 

39 

d 

9 

21 

42 

4-33 

0.29 

6.I7 

3.7 

12.6 

40 

b 

23-3 

46.6 

0-35 

6.85 

3-6 

13.2 

d 

25 

50 

4-45 

0.41 

7-35 

3-5 

13  6 

42 

b 

27 

54 

4-75 

0.31 

7  93 

3-7 

16.4 

43 

d 

3° 

60 

4.61 

0-57 

8  82 

3-4 

15.1 

44 

b 

33 

66 

4-95 

0.51 

9.70 

3-5 

18  i 

45 

ac 

35 

70 

4-77 

0-73 

10.29 

3  3 

16.5 

a  denotes  beams  rolled   by  Carnegie,  Cambria,  Jones  &  L..,  and  Phrenix;    6  by  Passaic;    c  by 

Penuoyd;    d  by  all  mills  (Includes  a,  b,  c). 

Note:-No.  31  by  Jones  &  L.,  and  Nos.   33,  35  and  37  by  Jones  &  L.  and  Cambria  are  rolled 
with  %  Ib.  less  metal  per  foot  than  weights  given  in  above  table. 


STEEL    I=BE,AMS—  Continued 

For  Beams,  Girders,  Columns,  or  Truss  Members              TABLE  17 

9 

IO 

II                   12                   13 

14 

15 

16 

Number 

Neutral  Axis  Co- 
incident with  Web 

Distance  C.  to  C. 
of  Webs  required 
to  make  Radii  of 
Gyration  Equal 

Allowable  End 
Reaction 

Web  in  Compres- 
sion. Allowable 
load  per  lin.  ft.  un- 
der Column  Base 
or  other  Load. 

Practical  Detailing 
Dimensions 

Radius  of 
Gyration 

Section- 
Moment 

Clear  dis- 
tance be- 
tween fil- 
lets on  web 

Flange 

K 

S       0 

Gage  of 
Rivet 
Lines 

N 

Inches 

Foot- 
Tons 

Inches 

Tons        Tons 

Inches 

Inches 

Inches 

i 

0.5 

0.26 

2.3           13.2 

3/8 

1% 

2 

3 

o'l 

o  29 
0.32 

H          "•{ 

4-o          3i-5 

lfi 

to 

to 

! 

4 

0.5 

0.23 

3-2 

I3-I 

5 

0.6 

0.38 

34 

14.0 

l/£ 

6 

0.6 

o  41 

4-7          20.4 

K 

to 

7 

0.6 

044 

6.1 

27.6 

i%£ 

8 

0.6 

0.44 

7.0 

^2.0 

9 

0.6 

0.46 

7-4         34-0 

2% 

10 

0.7 

0.54 

4  7 

14.8 

ii 

06 

0.61 

7-6 

26.6 

12 

0.6 

0.61 

8.1 

28  5 

\/ 

i?/ 

13 

0.7 

0.84 

5.8 

i9-3 

to 

to 

0.6 

0.69 

II.  2 

4i-3 

H 

2 

15 

0.7 

o  92 

85 

30.2 

3% 

16 

0.7 

0-75 

4-7 

5-9 

14.6 

17 

0.7 

0-74 

6.2 

15  5 

18 

0.7 

0.81 

9-4 

26.6 

19 

0.8 

1.04 

6.7 

17-5 

H 

JK 

20 

0.7 

088 

4-3 

12.9 

38.3           4% 

to 

21 

0.8 

I.  ii 

IO.O 

28.3 

2 

22 

0.8 

1.20 

13  5 

40.0 

23 

i.i 

3-2 

3 

H  to  K 

3 

24 

i.i 

25 

1.2 

4.6 

2^} 

3/  to  7A 

3/4 

26 

1.2 

27 

0.8 

I.O 

5*5 

7-9 

164 

28 

0.8 

I.O 

II.  0 

25  5 

H 

2 

29 

0.7 

I.I 

5-2 

14-5 

35-5 

5/8 

to 

to 

30 

0.9 

1.7 

ii.  3 

26.5 

# 

2X 

31 

0.8 

1*3 

6.3 

9.2 

17  i 

32 

0.9 

1.4 

ii-S 

21.7 

33 

0.8 

!-3 

13.0 

25-4 

2% 

34 

I.O 

1.8 

10.3 

19.0 

3^ 

to 

35 

0.8 

i-4 

6.0 

16.2 

33-5 

2/^ 

36 

o  9 

1.9 

14.4 

28.8 

37 

0.8 

i-5 

5-8 

19-5 

41.8 

6l/ 

38 

0.9 

2.0 

173 

362 

39 

09         1.6 

7-i 

105         17.8 

40 

0.9 

i.  7 

14.2 

23-4 

4i 

09 

17 

16.6 

28.8 

2>£ 

42 

i.i 

2-5 

11.9 

19.8 

X 

to 

43 

0.8           1.8 

23  i 

43-5 

24/ 

44 

I.O               2.8 

20.7 

38.0 

45 

0.8               2.O 

6-4 

29.6 

58.0 

7A 

STEEL   I=BEAMS 

For  Beams,   Girders,   Columns,  or  Truss  Members             TABLE  17 

I                  2 

3              4 

5 

6               7 

8 

i 

I 

Plr^ot                  Dimensions 

I 

d                Neutral  Axis 
.2  B         Perpendicular  to 

is          Web 

*& 

£*                     * 

^       0= 

i_ 

"d        B         •- 

|l 

o| 

,0d 

11      11      11 

a       t> 

c. 

PQ 

r       flB 

P^t^ 

3 

^•j  O                  c3  ^»                 g^^Tj 

!  '  1 

W 

H 

BO            ccS 

Inches      Lbs. 

Lbs. 

Inches 

Inches 

Square 
Inches 

Inches   i     Tons 

46          d 

IO 

25 

50         4-66        o  31         7.35          4.1 

16.3 

47          b 

27              54          4-81          0.37           7.93            4.0          17-0 

48          d 

30 

60          4.81 

0.46           8.82             3.9           17.9 

49           b 

33 

66          5.00          0.37          9.70            4.1           21.5 

50          d 

35              7°          4-95          0-60        10.29     i       3-8          19-5 

51           d 

40             80          5.10         0.75        ii  75           3.7          21.2 

52           d 

12 

3L5            63         5.00         0.35         9-26           4.8        24.0 

53           d 
54          d 

35              70          5-°9          0.44        10.29     j       4-7          25.4 
40            80         5.25         0.46       11.75          4.8         29.9 

55 

d 

45 

90          5-37:         0.58        13.22            4.6          31.7 

56 

d 

5° 

loo          5.49 

0.70         14.69 

4-5 

33-7 

57 

d 

55 

no          5.61 

0.82         16.16 

4-4 

35  7 

58 
59 

be 
be 

60 
65 

120              6  12 

130          6.25 

0^88 

17-63 
19.10 

4.6 

4-5 

41.7 

43-7 

60 

d 

15             42            84          5.50         0.41       12.34 

6.0 

39-3 

61 

d                          45             9°          5  55          0.46        13  22 

5-9 

405 

62 

d 

50           loo          5  65 

o  56         14.69 

5-7 

43  o    i 

63 
64 

d 

& 

no          5-75 
120         6.00 

066 
0.59 

16.16 
17.63 

5-6 
5-9 

454 
54-1 

65 

d 

65 

130          6.10          0.69         19.10     \        5.8 

56.5 

66 

d 

70 

140     |      6.19     j      o  78     I    20.57            5.7 

59° 

67 

d 

75 

150          629          0.88        22.04 

5.6 

61.4 

68 

d 

80 

lOo          6.40 

0.81      23.51 

5-8 

70.7 

69 

Came 

gie                85 

170          6.48 

0.89        24.98           5.7 

72  7 

70 

11 

90 

180          658          099        2645             5.6 

75  i 

',' 

95 

190          6  68           1.09        27  92             56 

77.6 

72 

" 

IOO               200              6.78              1.19           29.39                 5.5              800 

73 

d 

18 

55           no 

6.00 

0.46 

.6.10 

7.1 

58.9 

74 

d 

60                I2O 

6.10 

o  56 

17.63 

6*9 

62  4 

75 

d 

65                130 

6  18          0.64 

19.10 

6.8 

653 

76 

d 

70 

140 

6.26          0.72 

2057 

6.7          68.2 

77 

be 

75 

15° 

6.16          0.66 

22.O4 

70 

808 

78 

be 

80 

160 

6.38 

o  69 

23  51 

6.9 

83  8 

79 

c 

85 

170          7.00          0.74 

2498 

6.8 

852 

80 

c 

90 

180          7.08 

0.82 

2645 

6-7 

88.0 

81 

d 

20 

65 

130 

6.25 

0.50 

19.10 

7-8 

78.0 

82 

d 

70 

140 

6-33 

0.58 

20.57 

7-7 

813 

83 

d 

75 

150 

6  40 

o  65 

22.04 

76 

84.6 

84 

d 

80 

IOO 

7.00 

0.60 

23.51 

7-9 

97-8 

85 

d 

85 

170 

706 

0.66 

2498 

7.8 

100.  6 

86 

d 

90 

1  80 

7.14 

o  74 

26.45 

7-7 

103.9 

87 

ac 

95 

190 

7.21 

0.81 

27.92 

7.6 

107.1 

88 

ac 

IOO 

200 

7.28 

0.88 

29-39 

7-5 

110.4 

89 

ac 

24 

80 

160 

7.OO 

0.50 

23.51 

9-5 

116.0 

90 

ac 

85 

170 

7.07 

0-57 

24.98 

9-3 

120.5 

ac 

9° 

180 

7-13 

0.63 

26.45 

9-2 

124.4 

92 

ac 

95 

190 

7.19 

0.69 

27.92 

9.1 

128.3 

93 

ac 

IOO 

200 

7-25 

0-75 

29-39 

9.0 

132.2 

a  denotes  beams  rolled   by  Carnegie,  Cambria,  Jones  &  L.,  and  Phrenix; 
Pencoyd ;    d  by  all  mills  (includes  a,  b,  c). 


6  by  Passaic;    c  by 


STEEL    I=BE.AMS  —  Continued 

For  Beams,  Girders,  Columns,  or  Truss  Members               TABLE  17 

9             10 

II                  12                 13                 14                 15                 16 

Neutral  Axis  Co-    i 
incident  with  Web 

clSl         Is                IJ                Practical  Detailing 

•^'3:3  o1         W  ff             A                         Dimensions 
•  »3ra                                  fl  A 

"§ 

<->£«"         ~r             03          .  ,  ,#               Flange 

a  a         ®-®S         -SSs            o^         .2£^£    - 

1 

§1            11          11*1          ?|            -2|         "SgdS         agj£      Gage  of 

?S       11      5£s£     2*       #%    \  $%$*     *.s2    Rivet 

| 

{Jo            ocS 

s^ao              ^   !  e*Ki  i  gpts 

1 

Inches 

?oot- 
ons 

Inches   j     Tons        Tons        Inches      Inches 

Inches 

46 

I.O              2.O              7.9           12.  0            l8.6 

' 

47 

I.O                2.1                                    16.4             24.6 

48 

0.9                2.1 

20.7          32.4 

2/^ 

49 

i.i            3-1 

16.4          24.6 

X 

to 

50 

0.9           2.3 

27.0          45.2 

3 

5' 

0.9 

2-5 

7-i          33-8          58-8           7/2 

52             i.o 

2.5              9.5            15.6           20.0 

53              I-° 

2.8                          23.8          28.5 

54              i-i 

3.5 

9.3    |    24.9        30.0 

55 

i.i 

3-7                          3i-3          4i.o 

X 

234 

56 

i 

3.9     |                      37.8          52.0 

to 

to 

57 

.0 

4.1            8.7          44.3          63.0           8-^ 

K 

3^ 

58 

2                 5-6                                     40.5              56.5 

59 

.2                 6.1 

47-5          68.5 

60 

., 

3-5 

11.7         19.1         22.3 

\ 

61 

.1                 3.6      i                               25.5              26.6                                                   | 

3 

62 

.0 

3-8                          37-2          36.0 

to 

63 
64 

.0 
.2 

4.0     !      ii.  i          44.6          45.0 
5.8          11.5         39.9        38.8         i\% 

\ 

3/2 

65 

.2 

6.0                           46.6          47.9 

X 

3/4 

66 

.2                 6.2                                     52.7              56.2 

to 

to 

67                .2            6.5           n.o     |      59.4          65.5                               7/z 

4 

68                .3           8.7          11.3        54.7         59  o 

• 

69                .3             9.0                           60.  i           66.0 

70                 .3             9-3                           66.9           75.0 

I 

to 

71                -3 

9-6                          73-6          84.5 

1 

4 

72                -3 

10.0           10.8           79.7           93.2          io3^ 

73                .2           4.7         14-0        22.4         23.4 

74                -I            4-9     !                      36-2          33-° 

75                .1            5.1                          49-4          40-0 

76                .1            5.2          13.2          58.3          47.6          14% 

^  '• 

3/4 

77                -3 

8.1 

46.2          46.0 

to  i 

to 

78 
79 

•3 

•3 

8.2 

8.4 

56.7         53-2 
59-9         48.5 

7/8  1 

4 

80               .3 

8-7 

66.4         56.0 

81                 .2           5.9 

15.5        25-0        25.0 

1 

82                      .2 

6.1                            39-9          32.5 

83                      .2 
84                      .4 

6-3 
8.7 

15-0         50-5          38.7 
15-5         41  8        34-2 

3/2 

85                -4            8.9 

51-7        39-5                       H 

to 

86                .4     i        9.1 

64.0      !        47.3 

4^( 

87                -3            9-4                          72.9          53-5 

88                .3            9.6          14.8          79.2          60.0     i       16 

89                .4           8.2 

l8.7            20.4             19.2 

90                .3            8.3 

30.9              26.O 

H 

3^ 

9i                -3            8.5 

42.3              32.0 

to 

to 

92                .3 

8.7 

54-5          37-5 

I 

4^2 

93                 -3            8.9           17.8          66.3           43.2         20^/2 

STEEL    CHANNELS 

For  Beams.  Girders,  Columns,  or  Truss  Members              TABLE  18 

I 

2 

3              4 

5 

6 

7 

8 

Weight 
per  foot 

Dimensions 

"3 

& 
a 

Neutral  axis 
Perpendicular  to 
Web 

0 

0 

a 

•»-=>      en 
C-    <» 

1 
a 

03 

9 

a 

is! 

CO 

1    t 

A 

1 

.0 

M 

^   1*   ff) 

g 

a 

rl 

1 

1 

1 

0 

fl«* 

o 

9 

cd 

^ 

& 

QQ 

o 

c  §   ^ 

t. 

o> 

g 

— 

6 

6 

P 

EH 

0 

co 

J^oo^ 

& 

£ 

M 

o 

cJ 

^ 

c3 

.£H 

s 

P 

I 

§ 

0 

EH 

1 

f 

•5 

i 

•1 

i 

Inches 

Lbs. 

Lbs. 

Inches 

Inches 

Square 
Inches 

Inches 

Foot- 
Tons 

I 

ac 

3 

4 

8 

.41 

0.17 

•17 

1.2 

0.7 

2 

ac 

5 

10 

•50 

26 

•47 

I.I 

0.8 

3 

ac 

6 

12 

.60 

36 

•76 

I.I 

0.9 

4 

b 

4 

5 

IO 

•59 

0.17 

•47 

1.6 

1.2 

5 

ac 

5-25 

10.5 

.58 

0.18 

•54 

1.6 

i-3 

6 

b 

6 

12 

.66 

0.24 

.76 

i.  5 

7 

ac 

6.25 

12-5 

•65 

0.25 

•  84 

1.5 

1.4 

8 

ac 

7-25 

H-5 

•73 

°-33 

2.13 

I.e 

z-5 

9 

b 

8 

16 

.86 

0.27 

2-35 

1.5 

1.8 

10 

b 

10 

20 

.01 

0.42 

2-94 

J-5 

2.1 

ii 

b 

5 

6 

12 

.66 

0.18 

1.76 

1.9 

i-7 

12 

ac 

6.5 

13 

.75 

0.19 

1.91 

1.9 

2.0 

13 

b 

8 

16 

.78 

0.30 

2-35 

1.8 

2.1 

14 

d 

9 

18 

.89 

0-33 

2.64 

1.8 

2-3 

15 

b 

10 

20 

•97 

0.31 

2.94 

1-9 

2-7 

16 

ac 

"•5 

23 

2.04 

048 

3.38 

2.8 

17 

b 

12 

24 

2.09 

o,43 

3-52 

1.8 

3-i 

18 

d 

6 

8 

16 

1.92 

0.20 

2.35 

2.3 

2.8 

19 

1. 

9 

18 

1-99 

0.25 

2.64 

2-3 

3  ° 

20 

b 

10 

20 

2  04 

o  30 

2  94 

2.2 

32 

21 

i'C 

10.5 

21 

2.04 

0.32 

308 

2.2 

3-3 

22 

b 

12 

24 

2.19 

0.28 

3-52 

2-3 

23 

d 

13 

26 

2.16 

0.44 

3-82 

2.1 

3-9 

24 

b 

15 

30 

2-34 

0-43 

4.41 

2.2 

4-7 

25 

ac 

15.5 

31 

2.28 

0.56 

4-56 

2.1 

4-3 

26 

b 

17 

34 

2.41 

0.38 

5.00 

2-3 

5-6 

27 

b 

18 

36 

2.46 

0-43 

5-29 

2-3 

5-8 

28 

b 

20 

40 

2.56 

0-53 

5.88 

2.2 

6.2 

29 

b 

7 

9 

18 

2.00 

O.2O 

2.64 

2-7 

3-6 

30 

ac 

9-75 

19-5 

2.09 

0.21 

2.86 

2.7 

4.0 

31 

b 

10 

20 

2.04 

O.24 

2-94 

2.6 

3.8 

22 

b 

12 

24 

2.13 

°-33 

3-52 

2.6 

4.3 

33 

ac 

12.25 

24-5 

2.20 

0.32 

3-6o 

2.6 

4-6 

34 

b 

13 

26 

2.22 

0.28 

3.82 

2-7 

5-2 

35 

ac 

14-75 

29.5 

2.30 

0.42 

4-34 

2-5 

5-2 

36 

b 

15 

2.30 

0.36 

4.41 

2.6 

5-6 

37 

b 

17 

34 

2-39 

0.45 

5.00 

2.5 

6.1 

38 

ac 

17.25 

34-5 

2.41 

0-53 

5.07 

2.4 

5-7 

39 

ac 

19-75 

39-5 

2.51 

0.63 

5.80 

2.4 

6-3 

a  denotes  beams  rolled   by  Carnegie,   Cambria,  Jones  &  L.,  and  Phoenix; 
Pencoyd ;    d  by  all  mills  (includes  a,  b,  c). 


by  Passaic;    c  by 


STEEL    CHANNELS—  Continued 

For  Beams,  Girders,   Columns,  or  Truss  Members                 TABLE  18 

9 

10 

II 

12                 13 

14 

15 

16 

i? 

Neutral  Axis  Parallel  with  Web 

Practical  Detailing  Dimensions 

d 

Flange 

Lattice  Bars 

© 
| 

adius  of  Gyration 

Section-Moment 
8  tons  per  D  " 
Max.  fibre  stress 

istance  of  Centre  of 
Gravity  from  Back  o 
Channel 

Distance  B.  to  B. 
required  to  make 
Radii  of  Gyration 
equal 

lear  Distance  Betwee 
Fillets  on  Web 

[aximum  Diam- 
eter of  Rivet 

age  of  Rivet  Lines 

T3   i  *0 

SoSId 

flip 

Mil!* 
Itlilla 

CO 

Flanges 
Out 

Flanges 
In 

ft 

M 

fi 

! 

O 

m 

0 

0 

[nches 

Foot- 

Inches 

Inches 

Inches 

[nches 

Inches 

Inches 

Ft.  and  Ins. 

W. 

Tons 

l 

0.41 

0.14 

0.44 

1-3 

2 

0.41 

0.16 

0.44 

y% 

Y& 

3 

0.42 

0.18 

0.46 

i.i 

1% 

4 

o.45 

0.17 

0.46 

2.0 

% 

5 

0.45 

0.19 

0.46 

6 

0.46 

0.45 

Y% 

7 

0.45 

0.21 

0.46 

to 

8 

0.46 

0.23 

0.46 

y* 

9 

0-55 

0.36 

0-59 

10 

0-55 

0.42 

0.60 

1.8 

2% 

J>8 

TI 

0.47 

O.2I 

0.45 

2.8 

4-6 

H 

12 

0.50 

0.25 

0.49 

'3 

0.46 

0.44 

y* 

H 

0.49 

0.30 

0.48 

15 

0.56 

0-57 

16 

0.49 

0.36 

0.51 

17 

0.56 

0-49 

0.58 

2.3 

4-6 

3'/s 

IT* 

18 

0.54 

0.33 

0.52 

3.5 

5.6 

yz 

! 

\yz"  x  #" 

19 

0-55 

051 

C.  toC:— 

20 

0-54 

0.50 

Mx.o'—  ii)4" 

21 

o-53 

0.38 

0.50 

Mn.o'-6^" 

22 

0.63 

O.6O 

0.65 

23 

0-53 

0-43 

0.52 

24 

0.63 

0.65 

25 

0-53 

0.49 

0-55 

4^8 

26 

0.70 

0.98 

0.78 

y* 

27 

0.71 

0-79 

to 

28 

0.72 

I.  II 

0.80 

2.6 

5-8 

# 

*H 

29 

0.56 

0-37 

0.51 

4.3 

6-3 

^ 

ilA 

i^"  x  X"  ' 

3° 

0.59 

0.42 

o.55 

C.  toC:— 

o-55 

0.50 

i 

MX.  I  -iW 

32 

0.54 

0.49 

Mn.  0-7^" 

33 

0.58 

0.47 

0-53 

34 

0.63 

0.63 

0.62 

35 

0-57 

0-53 

0-54 

36 

0.63 

0.62 

37 

0.63 

0.74 

0.62 

H 

38 

0.56 

0.58 

0.56 

tO             ll/2 

39 

0.56 

0.64              0.58 

3-5 

6.0 

5# 

* 

STEEL    CHANNELS 

For  Beams.  Girders,  Columns,  or  Truss  Members               TABLE  18 

, 

3               4 

5              6 

7 

8 

Weight                   Dimensions 

a 
a 

Neutral  axis 
Perpendicular  to 
Web 

; 

o 

1 

d-  8 

1 

"5 

+3 

S  !-'-£ 

i 

•   J9 

J 

d 

Q 

*H 

o  «*  * 

A 

® 

9 

31 

^» 

^  X  £^ 

o 

a 

£3 

T3 

M 

O 

O 

1    rr  ^ 

1 

B 

*o 
I 

A 

O 

1 

1 

03 

"o 

| 

II" 
1-3 

a 

1 

*S 

a 

£ 

oJ 

o 

£ 

*e3 

| 

w 

0 

H 

K 

^ 

•< 

tf 

M 

I 

Inches 

Lbs. 

Lbs. 

Inches 

Inches 

Square 
Inches 

Inches 

Foot- 
Tons 

40 

b 

8 

IO 

20 

2.08 

0.20 

2-94 

3-i            4-7 

b 

ii 

22 

2.12 

0.24 

3-23 

3.0            4.9 

42 

ac 

11.25 

22.5 

2.26 

0.22 

3-30 

3.1    i      5-4 

43 

b 

12 

24 

2-15 

0.27 

3-52 

3-°            5-3 

44 

b 

13 

26 

2.22 

0.25             3.82 

5-9 

45 

ac 

13-75 

27-5 

2-35 

0.31 

4.04 

3-o 

6.0 

46 

b 

15 

30 

2.29 

0.32 

4.41 

3-° 

6.4 

47 

ac 

16.25 

32.5 

2-44 

0.40 

4-77 

2-9 

6-7 

48 

b 

17 

34    . 

2-37 

0.40 

5.00 

2.9 

7.0 

49 

ac 

18-75 

37-5 

2-53 

0.49 

5-51 

2.8 

7-3 

50 

ac 

21.25 

42.5 

2.62 

058 

6.24 

2.8 

7-9 

5I 

b 

9 

13 

26 

2.36 

0.23 

3.82 

3-5 

6-7 

52 

ac 

13.25 

26.5 

2.43 

0.23 

3.89 

3-5 

7.0 

53 

b 

14 

28 

2-39 

0.26         4.  1  1 

3-4 

7.0 

54 

d 

15 

3° 

2.49 

0.29          4-41 

3-4 

7-5 

55 

b 

16 

32 

2.56 

o.  28          4.  76 

3-5 

8.4 

56 

b 

18 

36 

2.63 

o-35          5-29 

3-4 

9.0 

57 

ac 

20 

40 

2.65 

0-45 

5.88 

3-2 

9.0 

58 

b 

21 

42 

2-73 

0.45 

6.17            3-3 

9.9 

59 

ac 

25 

50 

2.82 

0.62 

7-35            34 

10.5 

60 

d 

IO 

15 

30 

2.60 

0.24 

4.4"           3.9 

8.9 

61 

b 

17 

34 

2.64 

0.29 

5.00           3.8 

9-5 

62 

b 

18 

36 

2.67 

0.32 

5-29            3-7 

9.8 

63 

d 

20 

40 

2-74 

0.38 

5-88            3.7 

10.5 

64 

d 

25 

5° 

2.89 

°-53 

7-35            3-5 

12.  1 

65 

d 

30 

60 

3.04 

0.68          8.81            3.4 

13-7 

66 

ac 

35 

70 

3-i8 

0.82 

10.29 

3-4 

15-4 

67 
68 

b 
ac 

12 

20 

20.5 

40 

2.88 
2.94 

0.28 
0.28 

5.88 
6.  02 

4.6 
4.6 

13-8 
14-3 

69 

b 

23 

46 

2-95 

0.35          6.76 

4-5 

15.0 

70 

d 

25 

50 

3-05 

0-39          7-35           4-4 

16.0 

71 

b 

27 

54 

3-13 

0.38 

7-93 

4-5 

17.8 

72 

d 

30 

60 

0.51 

8.81 

4-3 

17.9 

73 

b 

33 

66 

3^8 

0-53 

9-7P 

4-3 

20.2 

74 

d 

35               7o 

3-30 

0.64 

10.29 

4-2 

19.9 

75 

ac 

40              80             3.42 

0.76        11.75 

4-1 

21.9 

1 

76 

d 

15 

33 

66 

3.40 

0.40        9.70    i       5.6 

27.8 

77 

d 

35 

70 

3-43 

0.43        10.29           5-6 

28.5 

78 

d 

40 

80 

3-52 

0.52        11-75            5-4 

3°.9 

79 

d 

45 

90 

3-62 

0.62        13.22            5.3 

33-3 

80 
81 

d 
ac 

50 

55 

IOO 

no 

3-72 
3-82 

0.72 
0.82 

14.69 
16.16 

5-2 

5-2 

35-8 
38.3 

a  denotes  beams  rolled   by  Carnegie,  Cambria,  Jones  &  L.,  an*t  Phoenix;    &  by  Passaic;    c  by 
Pencoyd;    d  by  all  mills  (includes  a,  b,  c). 


STEEL    CHANNELS—  Continued 

For  Beams.  Girders,   Columns,  or  Truss  Members                TABLE  18 

9 

10 

ii 

12 

13 

14 

15 

16 

i? 

Neutral  Axis  Parallel  with  Web 

Practical  Detailing  Dimensions 

<M 

| 

d 

Flange 

Lattice  Bars 

0 

$ 

"§-  K 

1$M 

Distance  B.  to  B. 

V 

fe 

m 

| 

llg 

fl 

O  o 

«£ 

required  to  make 
Radii  of  Gyration 
equal 

ance  Beti 
n  Web 

i|| 

Lvet  Line! 

:              n3  ^"S 

|lj|3 

1 

o 

ill 

ill 

^o 

6| 

|S 

I'S 

PH 
O 

Ifflli 

* 

& 

a 

P 

CO     »ej 

-w  *^*G 

Flanges 

Flanges 

fea 

"H  ® 

<D 

Vfl 

N|-5S^-SS 

3 

cc^JO 

Out 

In           ^PR 

^"S 

I 

SQ 

K 

r« 

5 

pi 

0 

W 

Inches 

Foot- 
Tons 

Inches 

Inches 

Inches 

Inches 

Inches 

Inches 

Feet  and  Ins. 

40 

0.58 

0-43 

0.52 

5.0            7.1 

i'x 

—         X    y  g- 

41 

0.58 

0.51 

C.  toC:—  • 

42 

0.63  i     0.53 

0.58 

i 

MX.  i'-3" 

43 

0-57  i   i 

0.50 

Mn.  o'j-8^" 

44 

0.62 

0.60 

0.58 

45 

0.62 

;  0.58 

0.56 

# 

46 

!o.6i 

0-57 

47 

:o.6i 

0.63 

0.56 

48 

b.6i 

0.69 

0.58 

\y^ 

49 

0.60 

0.68 

0-57 

5° 

0.60 

0.74 

0-59 

4.2 

6-7 

6TV 

51 

0.64        0.61 

0-57 

5-7 

7-9 

"# 

2"  x  TV 

52 

0.67 

0.65 

0.16 

C.  toC:— 

53 

0.65 

o.57 

MX.  i  '-4)4" 

54 

0.67 

0.69 

0-59 

K 

Mn.  o'L9)4" 

55 

0.74 

0.91 

0.66 

! 

56 

0.72 

0.66 

i 

57 

0.65 

0.79 

o-59 

58 

10.71 

1.03 

0.66 

j 

i% 

i 

59 

0.64 

0.91          0.62            4.8 

7-6 

6^ 

, 

60 

6.72 

0.78 

0.64 

6.3 

8.9 

,i^ 

2"X:f£" 

61 

0.71 

0.62 

C.  toC:— 

62 

0.71 

0.61 

M 

MX.  i'-6)4" 

63 

19.70 

0.89 

0.61 

- 

Mn.  o'-io^" 

64 

0.68 

.00 

0.62 

65 

10.67 

.11 

0.65 

2 

66 

0.67 

;   -25 

0.70 

S-2 

8-3 

75/s 

67 

0-79 

;     .12 

0.69 

7-7 

10.4 

^ 

I& 

2#"  X  ^' 

68 

0.81         .17        0.70 

C.4toSC:— 

69 

0.78 

0.67 

MX.  i'-io)4" 

70 

0.79 

:     -27 

0.68 

Mn.  x'-i" 

71 

0.86 

.61 

0.78 

72 

0.77 

•39 

0.68 

73 

0.84 

o.77 

/4 

74 

0.76 

.51 

0.69 

to 

2lA> 

75 

0.75 

.64 

0.72 

6.6 

9.9 

9i\ 

% 

76 

0.91 

2.  II 

0.79 

9-5 

12.7 

•*1A 

2/4"  X    "5/g" 

77 

0.91 

2-I5 

0-79 

C.  to  C':— 

78 

0.89 

2.29 

0.78 

IT 

MX.  2'-2}4" 

79 

0.88 

2.42 

0.79 

to 

Mn.  i'-3X" 

80 

0.87 

2-57 

0.80 

H 

2)4 

81 

0.87 

2.72 

0.82 

8-5 

11.7      ii^ 

PLATE,    AND     CHANNEL    COLUMNS 

(Supplement    to    Table     18)                               TABLE  19 

• 

2 

3 

4 

5 

6 

I 

2 

3 

4 

5           0 

6"  CHANNELS 

7"  CHANNELS 

8"  Plates 

9"  Plates 

9"  Plates 

11"  Plates 

Weight 
of  each 
Channel 

Thickness 
of  Plates 

1 

Least 
Badius  of 
Gyration 

Weight  of 
Column 

Kadius  of 
Gyration 
equal  on 
both  Axes 

Weight 
of  each 
Channel 

Thickness 
of  Plates 

Weight  of 
Column 

Least 
Badius  of 
Gyration 

il 

Badius  of 
Gyration 
equal  on 

both  Axes 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft. 

[nche: 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft 

Inches 

Lbs. 
per  ft. 

Inches 

3 

* 

29.6 

2-3 

2-7 

9-75 

X 

34-8 

2.6 

38.2 

3-2 

rV 

33-° 

35-1 

38.6 

42.9 

y* 

36.4 

39-0 

y* 

42.5 

47-6 

yV 

39-8 

42.8 

yV 

46.3 

52.2 

^ 

43-2 

46.6 

1/2 

50.1 

56.9 

A 

46.6 

50-4 

& 

53-9 

615 

# 

50.0 

2-3 

54-3 

2.7 

57-8 

2.6 

66.3 

3-3 

10.5 

¥ 

34  6 

2-3 

36.3 

2-7 

12.25 

K 

39-8 

2-5 

43-2 

3-i 

38.0 

40.1 

A 

43-6 

47-9 

y$> 

41.4 

44.0 

y?> 

47-5 

52.6 

7 

44.8 

47-8 

A 

57-2 

K 

48.2 

51.6 

% 

55-i 

61.9 

51.6 

55-4 

& 

58.9 

66.5 

s 

55-° 

2-3 

59-3 

2.6 

4 

62.8 

2.6 

71-3 

3-3 

13 

X 

39-6 

2.2 

41-3 

2-5 

14-75 

# 

44-8 

2-5 

48.2 

3.0 

yV 

43-° 

TZ 

48.6 

52.9 

y& 

46.4 

49.0 

y& 

52.5 

57-6 

yV 

49-8 

52.8 

A 

56.3 

62.2 

^ 

S3-2 

56.6 

H 

60.  i 

66.9 

y9F 

56.6 

60.4 

y9g" 

63-9 

71-5 

>£ 

60.0 

2.2 

64.4 

2.6 

H 

67.8 

2-5 

76.3 

3-3 

15.5 

X 

44-6 

2.  I 

46.3 

2.5 

17.25 

tf 

49.8 

2.4 

53-2 

2.9 

TS 

48.0 

50.1 

A 

53-6 

57-9 

y% 

5^4 

54-0 

^8 

57-5 

62.6 

7 
TTT 

54*8 

57-8 

A 

61.3 

67.2 

58.2 

61.6 

¥ 

65.1 

71.9 

y9F 

61.6 

65-4 

68.9 

76-5 

# 

65.0 

2.2 

69-3 

2.6 

H 

72.8 

2-5 

8i-3 

3-2 

19.75 

^ 

54-8 

2.4 

58.2 

2.9 

5 

58.6 

62.9 

y?> 

62.5 

67.6 

T7(T 

66.3 

72.2 

i^ 

70.1 

76.9 

T9tT 

73-9 

8i.5 

N 

77-8 

2.4 

86.3 

3-2 

PLATE-    AND     CHANNEL    COLUMNS    (Continued) 

(Supplement    to    Table     18)                               TABLE  19 

I 

2 

3 

4 

5 

6 

I 

2 

3 

4 

5 

6 

8"  CHANNELS 

9"  CHANNELS 

10"  Plates 

12"  Plates 

11"  Plates 

13"  Plates 

Weight 
of  each 
Channel 

Thickness 
of  Plates 

11 

Ss 

Least 
Badius  of 
Gyration 

Weight  of 
Column 

ill 

Weight 
of  each 
Channel 

ll 

i® 

ofl 
|1 

Least 
Badius  of 
Gyration 

"o  a 

S| 

|||l 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft. 

Inche; 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft. 

[nchee 

Lbs. 
per  ft 

Inches 

Lbs. 
per  ft. 

Inches 

11.25 

* 

39.5 

3-0 

42.9 

3.6 

13.25 

,/ 

45-2 

3.3 

48.6 

4-1 

•  TK 

43-7 

48.0 

A 

49-9 

54.i 

y* 

48.0 

53.1 

3/8 

54-6 

59.7 

T^B 

52.3 

58.2 

A 

59-2 

65.2 

X 

56.5 

63.3 

63.9 

70.7 

TS 

60.8 

68.4 

9 

68.5 

76.2 

H 

65.0 

2.9 

73-5 

3-7 

H 

73-3 

3-3 

81.7 

4.0 

13.75 

If 

44-5 

2.9 

47-9 

3-5 

15 

#  " 

48.7 

3-3 

52-1 

4.0 

TS 

48.7 

53-o 

53-4 

57-6 

|4 

53-0 

58.1 

r 

58.1 

63.2 

& 

57-3 
61.5 

63.2 
68.3 

$ 

62.7 
67.4 

68.7 
74-2 

T91 

65.8 

73-4 

T9ft 

72.0 

79-7 

H 

70.0 

2-9 

78.5 

3-6 

H 

76.8 

3-3 

85.2 

4.0 

16.25 

3S/ 

49-5 

3-0 

52.9 

3-4 

20 

x 

58.7 

3-2 

62.1 

3-8 

T*V 

53-7 

58.0 

T% 

63-4 

67.6 

y% 

58.0 

63.1 

y& 

68.1 

73-2 

T7ir 

62.3 

68.2 

A 

72.7 

78.7 

K 

66.5 

73-3 

yz 

77-4 

84.2 

T9ff 

70.8 

78.4 

T9? 

82.0 

89.7 

>£ 

75-° 

3.° 

83.5 

3-6 

H 

86.8 

3-2 

95.2 

3-9 

18.75 

# 

54-5 

2.8 

57-9 

3.3 

25 

X 

68.7 

3-i 

72.1 

3-6 

T*V 

58.7 

63.0 

•j-V 

73-4 

77.6 

H 

63.0 

68.1 

N 

78.1 

83-2 

T71T 

67.3 

73-2 

TT 

82.7 

88.7 

8 

71-5 

78.3 

87.4 

94-2 

T9ff 

75-8 

83-4 

y9T 

92.0 

99-7 

H 

80.0 

2.8 

88.5 

3.6 

M' 

96.8 

3-i 

105.2 

3-9 

21.25 

tf 

59-5 

2.7 

62.9 

3-3 

T5F 

63-7 

68.0 

fi 

68.0 

73-  I 

A 

72.3 

78.2 

yz 

76.5 

83-3 

T9?r 

80.8 

88.4 

j» 

85.0 

2.8 

93-5 

3-6 

PLATE.    AND     CHANNEL    COLUMNS    (Continued) 

(Supplement    to    Table     18)                               TABLE  19 

I 

2 

3 

4 

5 

I 

6 

i 

2 

3 

4          5 

6 

10"  CHANNELS 

12"  CHANNELS 

12"  Plates 

15"  Plates 

14"  Plates 

16"  Plates 

Weight 
of  each 
Channel 

Thickness 
of  Plates 

Od 

•ga 
§1 
P 

Least 
Badius  of 
Gyration 

"Sd 

11 
P 

itadius  ul 
Gyration 
equal  on 
both  Axes 

•43  '-'3 

III 

"£^$2 
£og 

Thickness 
of  Plates 

"oc 

II 
p 

Least 
Badius  of 
Gyration 

Ofl 

11 
P 

3fld$ 

33-2  OX 

fill 

$$»,£ 

Lbs. 
per  ft. 

[nches 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft. 

Inches 

Lbs. 
per  ft 

Inches 

Lbs. 
per  ft. 

Inches 

15 

X 

5°-4 

3-6 

55-5 

45 

20.5 

X 

64.8 

4-4 

68.2 

5-2 

A 

55-5 

61.9 

& 

70.8 

75-0 

#' 

60.6 

68  T> 

y* 

76.7 

81.8 

65.7 

74-6 

A 

82.7 

88.6 

K 

708 

81.0 

^ 

88.6 

95-4 

A 

75-9 

87.4 

& 

94.6 

102.2 

& 

81.0 

3-5 

938 

4.6 

H 

100.5 

4-3 

lOQ.O 

5-° 

20 

X 

60.4 

3-5 

65-5 

4-3 

25 

% 

738 

4-4 

77-2 

5-1 

A 

65.5 

71.9 

& 

798 

840 

3A 

70.6 

783 

H 

85-7 

90.8 

7 
Iff 

75-7 

846 

TV 

91.7 

97.6 

% 

80.8 

91.0 

% 

97.6 

104.4 

T9* 

85-9 

974 

T9« 

103.6 

III.  2 

rf 

90.1 

3-5 

103.8 

4.6 

H 

109.5 

4-3 

118.0 

5-o 

25 

X 

70.4 

3-4 

75-5 

4-' 

30 

X 

83.8 

4-3 

87.2 

4-9 

T\ 

75-5 

81.9 

5 
T7T 

89.8 

90.4 

3/8 

80.6 

88.3 

H 

95-7 

100.8 

A 

85-7 

94-6 

i 

TH 

101.7 

107.6 

K 

90.8 

IOI.O 

% 

107.6 

114.4 

A 

95-9 

107.4 

& 

113.6 

121.  2 

N 

IOI.O 

3-4 

113.8 

4.6 

H 

"9-5 

4-2 

128.0 

5-° 

30 

% 

80.4 

3-3 

85-5 

4.0 

35 

X 

938 

4.2 

97.2 

4-8 

T6ff 

85.5 

91.9 

A 

99-8 

104.0 

3/8 

90.6 

98.3 

X 

105-7 

1  10.  8 

A 

95-7 

104.6 

TW 

in.  7 

117.6 

3 

100.8 

III.O 

^ 

117.6 

124.4 

A 

105.9 

117.4 

T9.T 

123.6 

131.2 

H 

III.O 

3-4 

123.8 

4-5 

H 

129.5 

4.1 

138.0 

4-9 

35 

X 

90.4 

3-3 

95-5 

3-9 

40 

X 

103.8 

4.1 

107.2 

4-7 

T5* 

95-5 

101.9 

TB« 

109.8 

114.0 

x 

100.6 

108.3 

3/8 

"5-7 

120.8 

TV 

105-7 

114.6 

TV 

121.7 

127.6 

% 

1  10.  8 

121.  0 

K 

127.6 

134.4 

& 

"5-9 

127.4 

A 

133-6 

141.2 

% 

121.  0 

3-3 

133-8 

4-4 

% 

139-5 

4-1 

148.0 

4-9 

tl) 

•J    « 

O  3 
O^ 


& 


sexy 
uo 


I        OQ       1 
I        <D 


JO  W 


jo  ^q 


^"  VO  00    O 

rn  O  f^  *o  cs 


S9xy  q'4oq 

UO 


JO  ^q 


I 


a§ 


CO        co 
10          10 


rho  oo  O  c<  TJ- t>.       ri-vo  oo  O  N  ^- 1^ 
M   ,CO  co  •*  LO  10 VO          CO  ••*•  rh  too  O   t-. 


uo 

UO 

jo  sni 


jo  snippy; 


jo  ^q 


jo 


1C 


tvo-ri-t 

M    (S    CO  'Jj-  1O 


•*VO  OO    O 

C7NO    COW 


O    M   rl- 


1C 


(101) 


STEE.L  ANGLES—  (E,ven  Legs) 

For  Beams,  Girders,  Columns,  or  Truss  Members               TABLE  20 

I 

2 

3 

4 

5 

6 

7 

8 

9 

IO 

II 

12 

13 

14 

1 

Weight  per  Foot 

"o 

NeutralAxis 
on  Line  45° 
to  Legs 

Neutral  Axis 
Perpendicular  to  Leg 

o 

Gages 

§ 

# 

O 
03 

A 

© 

] 

TD 

°£ 

-£  fcD 
OQ^ 

%i! 

Sw 

O  CD 

tf-u 

111 

Radius  of 
Gyration 

go 

is 

i 

O  bo 

QQ 

QQ 

O 

a 
M 

a 

© 

o 

o 

(J 

•31 

h 

«M    O 

°a§ 

if 

c  . 

Iv 

®  rt    • 

.go 

3it 

^ 

§Tl 

53 

III 

1 

a 
0 

1 

I 

c 

$$ 

s 

M« 

o3<3 

|t« 

53  I 

1 

all 

Inches 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Square 
Inches 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Foot- 
Lbs. 

In. 

Inches 

I       XI 

y% 

0.8 

1.6 

3-2 

0.24 

O.2O 

0.42 

0.30 

0.31 

0.62 

4i 

3/8 

A 

A 

1.2 

2-3 

4.7 

0.34 

58 

X 

i-5 

6.0 

0.44 

0.19 

0.48 

0-34 

0.29 

0.66 

74 

iX*iX 

1A 

1.0 

2.O 

4-i 

0.30 

0.25 

0.50 

0-35 

0.38 

0.72 

65 

X 

X 

A 

i-5 

3-o 

5-9 

0.43 

94 

X 

1.9 

3.8 

7.6 

0.56 

121 

A 

2.4 

4.7 

9-3 

0.68 

0.23 

0.60 

0.42 

0.36 

0.77 

145 

I^XI^ 

# 

1.2 

2.5 

4-9 

o  36 

0.30 

o  60 

0.42 

0.46 

0.83 

93 

# 

ft 

T83 

1.8 

3.6 

7-2. 

0-53 

138 

X 

2.4 

4-7 

94 

0.69 

178 

2.9 

5-7 

11.4 

0.84 

216 

H 

3-4 

6.7 

13-4 

099 

0.29 

0.72 

0.51 

0.44 

0.88 

253 

iXXIX 

A 

2.1 

4-2 

8.4 

0.62 

035 

0.72 

O5i 

0.54 

0-93 

186 

% 

i 

X 

2.8 

5-5 

II.  0 

0.81 

253 

A 

3-4 

6.8 

13-6 

1.  00 

306 

?4 

4.0 

8.0 

I5.9 

1.1,7 

346 

x 

4.6 

9-2 

18.3 

1.30 

0-33 

0.83 

0.59 

0.51 

0.98 

400 

2       X2 

A 

2-5 

5  o 

10.0 

0.72 

0.40 

0.80 

0-57 

0.62 

1.03 

253 

y& 

i# 

X 

3-2 

64 

12.8 

0.94 

333 

6 

4.0 

80 

16.0 

•15 

400 

M 

4-7 

9-4 

18.8 

•36 

467 

A 

53 

10.6 

21.2 

.56 

0-39 

0-93 

0.66 

0-59 

i.  08 

533 

2X*2X 

A 

2.8 

5.6 

II.  2 

0.81 

0.44 

0.89 

0.63 

0.70 

1.  12 

320 

X 

JX 

Special 

X 

3-7 

7-4 

14.8 

.06 

426 

4-5 

9.0 

18.0 

.31 

520 

3/6 

5-3 

10.6 

21.2 

•55 

600 

A 

6.1 

12.2 

24.4 

•78 

693 

6.8 

13.6 

27.2 

2.OO 

o.43 

1.05 

0.74 

0.66 

I.I9 

773 

2^X2^ 

A 

3-i 

6.2 

12.4 

0.90 

0.49 

0.98 

0.69 

0.78 

1.22 

400 

X 

«H 

X 

4-i 

8.2 

16.4 

I.I9 

533 

5  o 

10.0 

2O.  O 

1.47 

640 

3^ 

5-9 

n.8 

23.6 

i-73 

760 

A 

6.8 

13.6 

27.2 

2.OO 

866 

7-7 

154 

30.8 

2.25 

0.47 

I-I5 

0.81 

0.74 

1.29 

973 

23^x2  3^ 

X 

4-5 

9-o 

18.0 

I-3I 

0-55 

1.  10 

0.78 

0.85 

1-34 

640 

X 

m 

Special 

5-5 

II.  0 

22.  0 

1.62 

786 

3/8 

6.6 

13.2 

26.4 

1.92 

920 

A 

7-6 

15  2 

30.4 

2.22 

1050 

8-5 

17.0 

34-0 

2.50 

0.52 

1.23 

0.87 

0.82 

i-39 

1180 

3     *3 

X 

4-9 

9.8 

19.6 

1.44 

0-59 

1.19 

0.84 

0-93 

1-43 

773 

ft 

iX 

A 

6  i 

12.2 

24-4 

1.78 

946 

H 

7-2 

14-4 

28.8 

2.  II 

IIOO 

A 

8-3 

166 

33-2 

2-43 

1260 

9-4 

18.8 

376 

2-75 

1420 

A 

10.4 

20.8 

41.6 

3.06 

1580 

N 

ii.  4 

22.8 

45-6 

3-36 

o-57 

1.41 

I.OO 

0.88 

I-5I 

1730 

Above  angles  are  rolled  by  nearly  all  mills. 


STEE,L   ANGLES—  (E,ven  Legs)—  Continued. 

For  Beams,   Girders,   Columns,   or  Truss  Members                TABLE  20 

I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

II 

12 

13 

14 

13 

Weight  per  Foot 

•3 

Neutral  Axis 
on  Line  45° 
to  Legs 

Neutral  Axis 
Perpendicular  to  Leg. 

1 

Gages 

§ 
02 

Thickness  of  M 

One  Anglo 

03 
& 

To 

(3 

o 
H 

Four  Angles 

Area  of  Sectior 
One  Angle 

Perpendicular 
Distance  from 
C.  G.  to  Back 

Eadius  of 
Gyration 

Section-Moment 
(Single  Angle) 

Max.  Size  of  E 

Single  and 
Double  Lines  of 
lUvets  in  Leg 

Basins  of 
Gyration 

Distance  from 
C.  G.  to  Apex 

If 

fi  a 

02  <! 

H* 

Inches 

Ins. 

Lbs. 

Lbs, 

Lbs. 

.nches 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Foot- 
Lbs. 

In. 

Inches 

3^x3^ 

JL 

7-i 

14.2 

28.4 

2.09 

0.69 

1.4 

I.O 

i.  08 

1.65 

1300 

H 

2 

3A 

8.5 

17.0 

34-0 

2.48 

153° 

TV 

9.8 

19.6 

39-2 

2.87 

1760 

% 

ii.  i 

22.2 

44-4 

3-25 

1980 

A 

12.3 

24-6 

49-2 

3.62 

2  2OO 

13-6 

27.2 

54-4 

3.98 

24IO 

H 

148 

29.6 

59-2 

4-34 

26lO 

16.0 

32.0 

64.0 

4.69 

2810 

it 

17.1 

34-2 

68.4 

5-°3 

0.67 

1.6 

1.2 

1.02 

1.74 

3000 

4     x4 

A 

8.2 

16.4 

32-8 

2.40 

0.79 

1.6 

i.i 

1.24 

I.85 

1720 

tt 

*X 

9.8 

19.6 

39-2 

2.86 

2O2O 

i  }£—  I 

• 

Tv 

"•3 

22.6 

45-2 

3-31 

233° 

X 

12.8 

25.6 

51-2 

3-75 

2620 

A 

143 

28.6 

57-2 

4.18 

2920 

H 

15-7 

31-4 

62  8 

4.61 

3200 

H 

17.1 

34-2 

6,8.4 

503 

3480 

3/ 

18.5 

37-o 

74.0 

5-44 

3740 

H 

19.9 

39-8 

79.6 

5-84 

0.77 

1.8 

1-3 

I.I* 

1.94 

4OIO 

5    *5 

M 

123 

24.6 

492 

3  61 

0.99 

2.0 

1.4 

1.56 

2.27 

3220 

H 

23/4/ 

Special 

TV 

14-3 

286 

57-2 

4^18 

1 

3720 

X 

16.2 

32.4 

64.8 

4-75 

4200 

T*V 

iS.i 

36.2 

72.4 

5-31 

4690 

^ 

2O.O 

40.0 

80.0 

5.86 

5*5° 

TIT 

21.8 

43-6 

87.2 

6.42 

5600 

M' 

23.6 

47-2 

94-4 

6.94 

6050 

H 

25.4         50.8 

101.6 

7.46 

6470 

N 

27.2 

54-4 

108.8 

7-99 

6900 

If 

28.9 

57-8 

115.6 

8.50 

7320 

1 

30.6 

61.2 

122.4 

9.00 

0.96 

2-3 

1.6 

1.48 

2.38 

7730 

6     x6 

H 

14-8 

29  6 

59-2 

4-36 

1.19 

2-3 

1.6 

1.88 

2.66 

4710 

ft 

3/2 

yV 

17  2 

34-4 

68.8 

506 

5430 

2/4~2/4 

X 

19.6 

39-2 

78.4 

5-75 

6140 

T9iT 

21.9 

43-8 

87.6 

6-43 

6850 

yk 

24.2 

48.4 

96.8 

7.11 

• 

7550 

fi 

26.5 

53.0 

1  06.0 

7.78 

8230 

•^ 

28.7 

574 

114.8 

8-44 

8900 

it 

30-9 

61.8 

123.6 

9  09 

9530 

7/& 

33-1 

66.2 

132.4 

9-74 

10190 

if 

35-3 

70.6 

141.2 

1037 

10810 

1 

37-4 

74-8 

149.6 

II.  OO 

1.  16 

2.6 

1.8 

i.  80 

2-77 

11570 

8     x8 

Rolled 

£ 

26.4 
29-5 

52.8 
59-0 

105  6 
118.0 

7-75 
8.68 

1.58 

3-1 

2.2 

2.50 

3-49 

11170 

12450 

% 

4/4 

2  24~3/4 

by 
Carnegie 

if 

32.7 
35-8 

65.4 
71.6 

130.8 
143-2 

9.61 

iQ-53 

13720 
15000 

and 
Pencoyd 
only. 

if 

38.9 
42.0 
45-o 

77-8 
84.0 
90.0 

iS5  6 
168.0 
180.0 

11.44 
12  34 
J3  23 

16210 
17500 
18700 

i! 

48.0 

96.0 

192.0 

14.12 

19900 

51.0 

102.0 

204.0 

15.00 

21060 

IT(T 

54-o 

108.0 

216.0 

15-87 

22200 

1^ 

56.9 

II3.8 

227.6 

16.73 

i  -.55 

3-4 

2-4 

2  42 

3.60 

23400 

Above  angles  are  rolled  by  nearly  all  mills. 


STEEL    ANGLES—  (Uneven  Legs) 

For     Beams,     Girders,     Columns,     or    Truss     Members             TABLE  21 

I 

2 

3 

4 

5 

6 

7 

8 

9 

IO 

II 

12 

13 

14 

15 

1 

Weight  per  Foot 

0 

&f 

Long  Leg  Perpendicular 
to  Neutral  Axis 

Short  Leg  Perpendicular 
to  Neutral  Axis 

1 
OQ 

lickness  of  M 

One  Angle 

'wo  Angles 

our  Angles 

jj® 

,st  TIadius  of  i 
n  of  Single  A 

rpendicular 
stance  -from 
,  G.  to  Back 

Radius  of 
Gyration 

tion-Moment 
ngle  Angle; 

rpendicular 
stance  from 
G.  to  Back 

Kadius  of 
Gyration 

tion-Moment 
ngle  Angle) 

<D  © 

"ttbi 

ill 

<X>0> 

if 

ill 

H 

Erl 

PR 

fl 

|S 

£§c 

35 

H%» 

|i 

£5^ 

* 

^ 

££ 

0? 

Inches 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Sq. 
Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Foot- 

Lbs. 

Ins. 

Ins. 

Ins. 

Foot- 
Lbs. 

I;H?Xl 

% 

I.O 

2.O 

4.0 

0.28 

O.22 

0.44 

0.44 

80 

0.26 

0.29 

40 

Special 

X 

1.8 

3-6 

7-2 

o-53 

0.48 

I2O 

0.29 

66 

2       XI;H$ 

A 

2.1 

4-2 

8.4 

0.60 

031 

0.66 

0.63 

240 

0-35 

0.40 

120 

Special 

X 

2.7 

5-4 

10.8 

0.78 

0.69 

306 

0-37 

1  60 

2^X1^ 

* 

2-3 

4-6 

92 

0.67 

O.4O 

0-75 

0.72 

306 

0-37 

0-43 

146 

Special 

3-0 

6.0 

12.0 

0.88 

4OO 

186 

A 

3-7 

7-4 

I48 

.07 

480 

226 

H 

4-3 

8.6 

17.2 

.27 

560 

266 

10.0 

2O.O 

45 

640 

307 

>l 

5-5 

II.  0 

22.0 

•63 

0-39 

0.86 

0.71 

786 

0.48 

0.40 

346 

2^X2 

A 

2.8 

5-6 

II.  2 

0.81 

0.43 

0.76 

0.79 

1.29 

386 

0.51 

0.60 

0.97 

266 

X 

3-7 

7-4 

148 

.06 

506 

333 

A 

4-5 

90 

18.0 

.31 

626 

5-3 

10.6 

21.2 

55 

733 

480 

•A 

6.1 

12.2 

24.4 

.78 

826 

546 

6.8 

13.6 

27.2 

2.OO 

0.42 

0.88 

0-75 

1-35 

933 

0.63 

0.56 

1.04 

613 

3    x2 

X 

4.0 

8.0 

16.0 

I.I9 

0.43 

0-99 

0-95 

1.56 

720 

0.49 

0-57 

0-93 

333 

Special 

A 

5  o 

IO.O 

20  o 

1.47 

780 

426 

N 

5-9 

ii.  8 

23.6 

1-73 

1040 

493 

_7_ 

6.8 

13.6 

27.2 

2.00 

1180 

560 

)l 

7-7 

15-4 

30.8 

2.25 

0.43 

i.  08 

0.92 

1.61 

1330 

0.58 

0-55 

0.98 

626 

3       y^-Yz 

X 

4-5 

9.0 

18.0 

L3I 

0-53 

0.91 

0-95 

1.50 

746 

0.66 

o.75 

1.18 

533 

ft 

5-5 

II.  O 

22.  0 

1.62 

920 

653 

3* 

66 

13.2 

26.4 

1.92 

1080 

773 

7-6 

15.2 

30.4 

2.22 

1240 

880 

^ 

8.5 

17.0 

34-0 

2.50 

1380 

986 

A 

9-5 

19.0 

38.0 

2.78 

0.52 

1.02 

0.91 

1.56 

1530 

0.77 

0.72 

1-25 

1090 

3Xx2 

X 

4-3 

8.6 

17.2 

1-25 

0.45 

1.09 

1.04 

1.70 

840 

0.48 

o.57 

0.92 

346 

Special 

A 

5-3 

10.6 

21.2 

i-54 

I02O 

426 

H 

6.2 

12.4 

24.8 

1.83 

1210 

493 

7-2 

144 

288 

2.  II 

1400 

573 

/2 

8.1 

16.2 

32.4 

2.38 

1560 

640 

A 

9.0 

18.0 

36.0 

2.64 

0.44 

1.  21 

I.OO 

i.77 

1730 

0-59 

0-53 

0.99 

706 

3^x2^ 

X 

4-9 

9.8 

19.6 

1.44 

0-54 

I.  II 

1.  12 

1.76 

IOCO 

0.61 

0.74 

I.I3 

546 

5 

6.1 

12.2 

24.4 

1.78 

1240 

666 

H 

7.2 

14.4 

28.8 

2.  II 

1450 

786 

8-3 

16.6 

33-2 

2-43 

1680 

906 

X 

9-4 

18.8 

37-6 

2.75 

1880 

IOIO 

JL 

10.4 

20.8 

41.6 

3.06 

2080 

1  120 

ff$ 

11.4 

22.8 

45-6 

3.36 

2280 

I22O 

H 

12.4 

24.8 

49-6 

3.65 

o-53 

1.27 

1.  06 

1.86 

2460 

0.77 

0.67 

1.23 

1320 

Above  angles  are  rolled  by  nearly  all  mills. 


STEEL    ANGLES—  (Uneven  Legs)—  Continued 

For     Beams.     Girders,     Columns,     or    Truss     Members 

TABLE  21 

i 

2 

3 

4          5          6 

7 

8 

9         10 

ii 

12 

13 

M        15 

1 

Weight  per  Foot 

r 
£,2     Long  Leg  Perpendicular     Short  Leg  Perpendicular 
£**             to  Neutral  Axis                    to  Neutral  Axis 

i 

!§ 

•s 

0?        :           ^ 

"tie        TJ> 

1 

~2 

II 

if 

||| 

Radius  of 
Gyration 

|l 

|g| 

Radius  of 
Gyration 

§1 

CD 

« 

vm 
C3 

|       "-" 

•^  *>^ 

^5 

£    PQ 

*§•< 

3 

| 

O 

§ 

0  fl 

I 

"»fl 

11 

II 

ll| 

o'si 

gfl-2 
%&>. 

|| 

||l 

i! 

H 

^ 

•? 

J.2 

oc 

H<£      '$'&    |£§o 

00 

•% 

$'£ 

Inches 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Sa. 
Ins. 

Ins. 

Ins. 

Ins. 

Ins-     LbsV     lns- 

Ins. 

Ins. 

Foot- 
Lbs. 

3^x3 

T5<r 

6.6 

13.2 

26.4 

i.93 

0.63 

1.06 

1.  10  ;  1.71      1280 

0.81 

0.90 

1-39 

960 

H 

7-8 

15.6 

31.2 

2.30 

i   1510 

1130 

9.1 

18.2 

36.4 

2.65 

1720 

1300 

V 

10.2 

20.4 

40.8 

3.00 

i   1930  ! 

1460 

TS 

ii.  4 

22.8 

45-6 

3-34 

2140 

1610 

X 

12.5 

25.0 

50.0 

3.67 

2340 

1770 

13-6 

27.2 

54-4 

4.00 

253° 

1920 

7 

14.7 

29.4 

58.8 

4-31 

2730 

2050 

it 

15-7 

3L4 

62.8 

4.62 

0.62 

1.23 

1.04    1.81 

2930 

0.98 

0.85 

1.50 

220O 

4     x3 

I* 

7.1 

14.2 

28.4 

2.09 

0.65 

1.26 

1.27 

1.97 

1640 

0.76 

0.89 

1-34 

985 

y% 

8-5 

17.0 

34.o 

2.48 

1940 

1160 

yV 

9.8 

19.6 

39-2 

2.87 

2240 

1320 

^ 

ii.  i 

22.2 

44.4 

325 

2520 

1490 

T9ff 

12.3 

24-6 

49.2 

3-62 

2780 

1640 

^ 

13.6    27.2 

54-4 

3.98 

3070 

1800 

H 

14.8    29.6 

59-2 

4-34 

3320 

1940 

16.0 

32.0 

64.0 

4.69 

3570 

2090 

it 

17.1 

34-2 

68.4 

5-03 

0.64     1.44 

1.  21      2.08       3830 

0.94 

0.83 

1.45  !  2240 

| 

4     *3/4 

TV 

7-7 

15-4 

30.8 

2.25 

0.73 

1.18 

1.26 

1.91     1680 

0-93 

1.07 

i-59     1340 

Special 

3/8 

9.1 

18.2 

36-4 

2.67 

2000 

1570 

A 

10.5 

21.  0 

42.0 

3-09 

2390 

1800 

/^ 

11.9 

23.8 

47-6 

3-5° 

2570 

!    2O2O 

A 

13-3 

26.6 

S3-2 

3-90 

2860 

2240 

H 

14.6 

29.2 

58.4 

4.3° 

3130 

2450 

H 

15-9 

31.8 

63.6 

4.68 

3410 

2660 

17.2 

34.4 

68.8 

5.06 

3670 

2860 

it 

18.5 

37-0 

74.0 

5-43 

0.72 

1.36 

I.I9 

2.01 

3890 

i.  ii 

I.OI 

1.69       3320 

4^x3 

TS 

7-7 

15-4 

30.8 

2.25 

0.66 

i-47 

i-44 

2.26 

2O5O 

0.72 

0.88 

1.31      1010 

Special 

y% 

9.1 

18.2 

36-4 

2.67 

2440 

1170 

T7¥ 

10.5 

21.  0 

42.0 

3-°9 

2800 

1340 

^ 

11.9 

23-8 

47.6 

3-50 

3160 

1500 

13-3 

26.6 

53-2 

3-90 

3520 

1660 

14.6 

29.2 

58.4 

4-3° 

3850 

1820 

15-9 

3L8 

63.6 

4.68 

4180 

1980 

^ 

17.2. 

34-4 

68.8 

5.06 

4510 

1 

2130 

it 

18.5 

37-o 

74-0    5.43 

0.64 

1.65 

1.38 

2-35 

4820 

0.90 

0.81 

1.46    2280 

5     X3 

T* 

8.2 

16.4 

32.8 

2.40 

0.66 

1.68 

1.61 

2.52 

2520 

0.68 

0.85 

1.26       1000 

H 

9.8 

19.6 

39-2 

2.86 

2980 

1180 

T7S 

11.3 

22.6 

45-2 

3-31 

3440 

1360 

/^ 

12.8 

25.6 

5L2 

3-75 

3880 

!53° 

T93 

14.2 

28.4 

56.8 

4.18 

43  10 

1690 

y$> 

15-7 

31-4 

62  8 

4.61 

473° 

1850 

\\ 

17.1 

342 

68.4 

5-03 

2010 

x 

18.5 

37-0 

74.0 

5-44 

555° 

2170 

it 

19.9 

39-8 

79.6 

5-84 

0.64  ,  1.86 

i-55 

2.62 

5940 

0.86 

0.80 

1.37 

2320 

Above  angles  are  rolled  by  nearly  all  mills. 


STEEL    ANGLES—  (Uneven  Legs)-Continued 

For    Beams,    Girders,    Columns,    or    Truss    Members            TABLE  21 

« 

2 

3 

4 

5 

6 

7 

8 

9 

IO 

II 

12 

13 

14 

15 

1 

Weight  per  Foot 

"o 

h 

Long  Leg  Perpendicular 
to  Neutral  Axis 

Short  Leg  Perpendicular 
to  Neutral  Axis 

i 

00 

"8 

•3 

M 

0 

1 

CC 

Q) 

0  © 

11" 

?3 

3]? 

IN 
Pi 

73  o  o 

Badius  of 
Gyration 

Moment 
Angle) 

pj 

Badius  of 
Gyration 

11 

-g 

03  13 

1 

o 

g 

0 

So 

&K 

03  <D 
tttlf 

g.|fi 

c- 
11 

Hi 

•llo 

i^| 

If 

i? 

5 

CD  H 

^1» 

c_i  q^ 

i£9 
H 

H 

<1 

05  o 

3* 

£sd 

E«5 

% 

gJQ 

£gd 

5H 

^ 

aj^Q 

Inches 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Sq. 
Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Foot- 
Lbs. 

Ins. 

Ins. 

Ins. 

Foot- 
Lbs. 

5     X3K 

Iff 

8.7 

17-4 

34-8 

2.56 

0.76 

1-59 

1.61 

2.45 

2580 

0.84 

0.03 

1.51 

1360 

H 

10.4 

20.8 

41.6 

305 

3°5° 

1610 

12.0 

24.0 

48.0 

3-53 

3250 

1850 

Y* 

13-6 

27.2 

54-4 

4.00 

3990 

2080 

& 

3°-4 

60.8 

4-47 

443° 

2300 

ll 

16^8 

33-6 

67.2 

4-92 

4860 

2530 

18.3 

36.6 

73-2 

5-37 

5290 

2750 

ti 

I9,8 

39-6 

79-2 

5.81 

5710 

2960 

tj 

21-3 

42.6 

85.2 

6.25 

6110 

3160 

22.7 

45-4 

90.8 

6.67 

0-75 

1.79 

1-53 

2-55 

7510 

1.04 

0.96 

1.61 

3360 

6     x3^ 

H 

II.7 

23-4 

46.8 

3-42 

0.77 

2.04 

1.94 

3.00 

4330 

0.79 

0.99 

1-43 

1640 

A 

J3  5 

27.0 

540 

3-97 

5000 

1880 

15.3 

30.6 

61.2 

4-59 

5650 

2120 

T9ff 

17.1 

34-2 

68.4 

5-°3 

6300 

2360 

H 

18.9 

37-8 

75-6 

5-55 

6920 

2580 

H 

20.  6 

41.2 

82.4 

6.06 

7530 

28lO 

22.3 

44-6 

89.2 

6.56 

8i39 

3°3° 

il 

24.0 

48.0 

96.0 

7.06 

8730 

3240 

!/& 

25  7 

51  4 

102.8 

7  55 

9300 

3450 

if 

27-3 

54-6 

109.2 

8.03 

9890 

3650 

i 

28.9 

57.8 

115.6 

8.50 

0.74 

2.26 

1.85 

3.10 

10420 

1.  01 

0.92 

1.56 

3860 

6     x4 

N 

12.3 

24.6 

49.2 

2.61 

0.88 

1.94 

i.93 

2.92 

4420 

0.94 

1.17 

1.67 

2130 

7 
TIT 

H-3 

28.6 

57-2 

4.18 

5110 

2460 

* 

16.2 

32.4 

648 

4  75 

578o 

2870 

18.1 

36.2 

724 

6440 

3080 

^ 

20.0 

40.0 

80.0 

5.S6 

7080 

3480 

ii 

21.8 

43-6 

87.2 

6.41 

7710 

3680 

^ 

23-6 

47-2 

94-4 

6-94 

8330 

396o 

il 

25.4 

50.8 

101.6 

7-47 

8930 

4240 

27.2 

54-4 

108.8 

7-99 

9530 

4530 

il 

28.9 

57-8 

115.6 

8.50 

IOIIO 

4789 

i 

30.6 

61.2 

122.4 

9.00 

0.85 

2.17 

1.85 

3.02 

10700 

1.17 

1.09 

i.79 

5°5° 

7    *3/4 

15.0 

30.0 

60.0 

4.40 

0.89 

2.50 

2.26 

3-56 

6680 

0-75 

0-95 

1-38 

1960 

Special. 

V 

17.0 

34-o 

68.0 

5.00 

7570 

2160 

Rolled 

T9ff 

19.O 

38.0 

76  o 

5-59 

8440 

2400 

by 

5A 

21.  0 

42.0 

84.0 

6.17 

9300 

2630 

Carnegie 

8 

23.0 

46  o 

92.0 

6-75 

10130 

2850 

and 

24.9 

498 

99.6 

10950 

3080 

Pencoyd 

it 

26.8 

536 

107.2 

7.87 

11750 

3310 

only 

28.7 

57-4 

114.8 

8.42 

12570 

3520 

i! 

30-5 

60  i 

1  20.  2 

8-97 

1335° 

3730 

I 

32.3 

64,6 

129.2 

9-50 

0.88 

2.71 

2.10 

3-68 

14100 

0.96 

0.89 

1.50 

395° 

8     >6 

y 

23.0 

46.0 

92.O 

6.76 

i-34 

2.47 

2.56 

3-74 

10710 

i-47 

1.79 

2.48 

6410 

Pencoyd 
only 

1 

25.8 
28.7 

51.6 

57-4 

103.2 
II4.8 

7-59 
8.44 

11946 
13180 

7142 

7875 

tt 

31  7 

63-4 

126.8 

9-32 

14420 

8607 

33-8 

67.6 

135-2 

9-94 

15655 

9340 

if 

36.6 

73-2 

146.4 

10.76 

16890 

10070 

!/% 

39-5 

79  ° 

158.0 

11.62 

18127 

10805 

if 

42.5 

85.0 

I7O.O 

12.50 

19363 

H537 

i 

45-6 

91.2 

182.4 

i-37 

2.72 

2-53 

•3.00 

20600 

1.72 

1.77 

2.65   12270 

Above  angles  are  rolled  by  all  mills  except  as  noted. 


PLATE  AND  ANGLE  COLUMNS.—  (Supplement  to  Table  21.)  TABLE  22 

WITH  COVER  PLATES 
Weight  per  Lineal  Foot  of  Cross  Section  Including 
|  Angles,  Web  and  Cover  Plates 

5?5* 

*M 
*"* 

£H 

®s 

9 

tn 

5 

1 

irb 

T—  I 

45 

KJ 

1 
s 

•<*•  M    ONVO    •<$•         M    ONVO    TJ-  >-i 
OO    M    roVO*    O°N         N*    ^  Is*  O    rO 

vo  oo  ON  o  M        ro  •<*•  "•>  t^oo 

M    M    M    N    N          NNNMtt 

02 

5 

^ 
_b 

0 

S 

^5 

3 
1 

J8 

CO  ro  Tj-  Ti-  no        *OVO  VO   t-s  Is. 
r<S  ^  >OVO'   t~s.        OO"    ON  O    i-"    N 

vo  t^oo  o  o        M  N  Th  LOVO 

_      M      M      M      <N                NNNNN 

% 

S3 

cbS 

CCX5 

K!O> 
*£ 

^2 
Pi 

1 

CO 
iH 

2 
1 

3' 

to  xovo  vo  r^      oo  oo  Cs  Os  o 

ro  rf  10  VO   t>-       OO   O\  O    **    ro 

N    ro  •*  iOVO          t^OO   O    "-1    N 

b^kild 
JBAOQ  JO 

ssaujioiitx 
peuiquioQ 

>t    X^^t        X^^: 

MMMM               NNNNfO 

WITHOUT  COVER  PLATES 
Weight  per  Lineal  Foot  of  Cross  Section  Including  Angles  and  Web  Plate 

X"  Web  Plato 

s 
I 

s' 

^(t 

iH 

s 

a 

r-l 

d 
n4 

1 
3 

N    N  00    •*  O    N    -*fVO  OO 

fOMOOO    Tfi-iOO   ION 

OOC^^OMNMCO^- 

VOOOOOVO         ^OCCOM1*         OOONOOON    Tj-VO 

ci  cf\  10  M  vo  N       vo  to  i-I  oo'  >o       c\  r^>  ^  ci  cf\  t--»  ^-  M  od 
VO  O   r^OO  00   O\        t^OO   C\  ON  O         t^OO   ON  O   O   •-"   N   ro  ro 

M                                       M     M     M     !-(«»-» 

co  1-.  t^  ^  fO  «0        fO^t^^M         is.  t^  ro  0\tn  t^  ONM   ro 

00    rt-  O  VO    N  OO          N    OSVO    rOM          ThNOt>.iONOMs.^- 
10VO   t^  t^sOO  OO         t^  t^-00    ON  O          t^OO    ON  O^  O    <->    <-*   N    ro 

M     M 

1 

Pi 
ft 

* 

? 

^ 
H 

Lbs.  per  L.  ft. 

\oooovovo      voooow-^-      OOVONOOON  -*vo 

VOfOONiOQ^           O»^»ONON         fOMOOVOfOMOOiON 
lOVO  VO   fs.00  00          t^t^OO    ON  ON         r^OO  00    ON  O    M    HH    N    ro 

5 
ci 

H 

N  VO  VO  V£>    N    M          N    -^-VO  00    O         VO  VO    N  00    Tj-VO  00    O    N 

f^O\»Oi-it^fO         t^rJ-MOOVO          ONt^iONOt^-^J-NON 
lOtoVO   t^  fsOO         VO   t^OO  00    O-.        VO    t^OO    ON  O    O    n    N    N 

s 

b 

H 

OONNNOOOO         OOON    -^-VO 

O\vo"   N  OO"   CO  ON         fO  M  OO'   «O  N 
•^  iovo  vo  t^  i^       vo  t~»  t>«OO   ON 

M  ^» 

si 

Is 

«ls^Hsx«!s^  ^-SXHs^   ^*£x«!5«:$>*:£^ 

03 

<D      ® 

.HO  "a 
«  « 

CO                                        *R 

X                                    ro                             •* 

»0                                            XX 

vo                             vo 

I 

X5 

? 

X 

s 

6 

iH 

i-4 

1 
s' 

OOOONNOO          '^NVOO'^t-         NOMVO    TfOO          N  00    O    N    O    M 

O    Tj-  ON  r«-5VO          MI^MVOO          ONrf-O\  rOOO    N          M  VO    N    *-»  N   t^ 
fOrorO'^Tj-         cofO^^>O        rorj-rt-io  w->VO          ^  ^  10  ^OVO  VO 

5 

00 

NNVOVON         OOVOO    -^-00         VO    "d-VO    O  00    N         VO    N  VO  ^O    -^-vO 

OONVOO^"         ONrj-O\rot^        VOinVOt-i»OO         OO'sJ-ONT^-ONTj- 
Ncoro-rl-^        NcorOTh-^-        fOTf-Tl-xo  iovo         ro  rf  •*  to  iovo 

5 
6 

(S.IS.M    M   Is, 

10  ON  TJ-OO    M 
N    M    CO  CO  •* 

ii 

XHS^HSX    X<SH=X    <«H^-iS«    <R-SX-|S« 

m 

§® 
«  o^i 

OG       C 
<5 

X                        ? 

S                  ?                X                    ff 

co                            <r>                            ro                                 rh 

STEEL   TEES 

For  Beams,   Girders,   Columns,  or  Truss   Members 

TABLE  23 

I 

2 

3 

4               5 

6                7 

8 

9 

Dimensions  and  Weights 

Axis  Parallel 
with  Flange 

Axis  Coincident 
with  Stem 

ngo 

c 

•      fl 

45  §  be 

5 

^o 

1 

oi£ji 

1 

© 

1 

1 

£ 

^^ 

g 

§ 

E* 

s 

§ 

*S*>:eo 

2 

1 

O 

i 

i 

£ 

1 

§^•3 

1 

| 

§ 

1 

1 

1 

a 

9 

1 

.lol 

1 

1 

£ 

OQ 

^ 

-«j 

fl 

PH 

02 

PH 

CQ 

Ins. 

Ins. 

Lbs. 

SQ.  Ins. 

Ins. 

Ins. 

Foot-lbs. 

Ins. 

Foot-lbs. 

i 

I 

0.87 

0.26 

0.29 

0.29 

40 

0.21 

26 

i 

1.23 

0.36 

0.32 

0.29 

66 

0.21 

53 

*tf 

*# 

J-53 

045 

0.38 

o-37 

93 

O.26 

66 

!# 

2.04 

0.60 

0.40 

0.36 

J33 

0.27 

93 

*H 

1/4 

1.84 

0-54 

0.44 

c>-45 

146 

0.3I 

93 

!^ 

2.4 

075 

0.42 

0.49 

1  86 

034 

133 

13X 

JX 

3-6 

1.05 

0.91 

0-33 

200 

o  41 

293 

i# 

0.90 

0-54 

0.51 

253 

0.37 

186 

2 

!^ 

3-i 

0.90 

0.42 

0.42 

200 

o-45 

240 

2 

3-7 

i.  08 

0-59 

0.60 

330 

0.42 

240 

2 

4-3 

1.26 

0.63 

0.60 

440 

0-43 

306 

2X 

2^ 

4.1 

1.20 

066 

0.67 

426 

0.47 

293 

2^ 

4-9 

1.44 

0.69 

0.68 

560 

0.48 

400 

2% 

1^ 

2.9 

0.84 

0.29 

0.31 

120 

0.58 

306 

2^        5-5 

1.62 

0.74 

0.74 

666 

052 

466 

2^            64 

1.89 

0.76 

0.74 

786 

°-53 

560 

2^1        5  8 

I-7I 

0.83 

083 

800 

051 

466 

6  7 

087 

084 

972 

0.58 

706 

3 

6.1 

1.  80 

o  92 

0.94 

IOIO 

0.51 

466 

3            7-2 

2.IO 

0.97 

0.92 

1160 

0.51 

573 

2% 

2            7.4 

2.16 

o-53 

0.71 

looo          0.54 

600 

3 

2#            6.1 

1.  80 

0.68 

0-73 

693 

0.65 

666 

2^            7-2 

2.10 

o  71 

o  72 

800 

0.66 

800 

3"         6.6 

i-95 

0.86 

0.90 

985 

0.62 

666 

3             7-8 

2.28 

0.88 

o  90 

1140 

0.63 

800 

3 

9.1 

2.67 

0.92 

o  90 

1340 

0.64 

960 

3 

IO.O 

2.94 

093 

0.88 

1460 

0.64 

1070 

85 

2.49 

.09 

.09 

1610 

0.61 

826 

3% 

9.8 

2.88 

.11 

.08 

1825 

0.68 

1170 

3% 

10.9 

3.21       |           .12 

.06 

1980 

0.62 

1070 

4 

9-3 

2-73 

.29 

.26 

2090 

0-59 

826 

4 

10.6 

3.12 

•32 

•25 

2370 

0.60 

960 

4 

ii.  8 

3.48 

•32 

•23 

2580 

o-59 

1080 

As  there  is  no  uniform  standard  for  Tees,  the  Carnegie  rolls  are  given  as  representative 
for  variety  of  size  and  weight. 

(108) 


STEEL    TEES—  Continued 

For  Beams,  Girders,  Columns,  or  Truss  Members 

TABLE  23 

I 

2 

3             < 

5 

6               7 

8 

9 

Dimensions  and  Weights 

Axis  Parallel 
with  Flange 

Axis  Coincident 
with  Stem 

- 

JJf 

§ 
53 

"fl 
<» 

1 

1 

1 

«~.t5 

1 

g 

I 

1 

I 

fil 

1 

a 
o 

1 

i 

1 

i 

C/Q 

*© 

1 

|o§ 

1 

1 

i 

1 

Ins. 

Ins. 

Lbs. 

Sq.  Ins. 

Ins. 

Ins. 

Foot-lbs. 

Ins. 

Foot-lbs. 

3^ 

3 

7-8 

2.28 

0.78 

0.89 

960 

0.76 

906 

3 

8.5 

2-49 

0.83 

0.88 

1170 

0-75 

1080 

3 

10.9 

3.21 

0.88 

0.87 

1500 

o.77 

H40 

3l/4 

9.2 

2.70 

1.  01 

1.05 

1590 

0-73 

1080 

3)4 

ii-7 

3-45 

i.  06 

1.04 

2025 

0.74 

1440 

4 

9-9 

2.91 

1.19 

1.22 

2060 

0.70 

jo8o 

4 

12.8 

3-75 

1-25 

1.  21 

2640 

0.72 

1440 

4 

2 

6.6 

1-95 

0.51 

0.51 

454 

0.95 

1170 

2 

7-"9 

2.31 

0.48 

0.52 

534 

0.96 

1400 

2)4 

7-3 

2.16 

0.60 

O.7O 

733 

0.91 

1170 

2)4 

8.6 

2.52 

0.63 

0.69 

826 

0.92 

1400 

3 

9-3 

2-73 

0.78 

0.86 

1170 

0.88 

1400 

4 

10.9 

3-21 

.15 

.23 

2180 

0.84 

1454 

4 

13-7 

4.02 

.18 

.20 

2690 

0.84 

1870 

4/4 

ii.  4 

3.36 

.31 

•38 

2640 

0.80 

1410 

4/4 

14.6 

4.29 

•37 

•37 

3400 

0.81 

1880 

5 

12.  0 

3-54 

•51 

•56 

3740 

0.78 

1410 

5 

15-6 

4-56 

•56 

•54 

4140 

0.79 

1880 

4K 

2^ 

9-3 

2.79 

0.60 

0.68 

866 

i.  08. 

1840 

2)4 

8.0 

2.40 

0.58 

0.69 

746 

1.07 

1546 

3 

IO.O 

3.00 

0-75 

0.86 

1250 

1.04 

1840 

3 

8-5 

2-55 

0-73 

0.87 

1080 

1.03 

1546 

3^ 

15.8 

4-65 

i.  ii 

1.04 

2840 

0.90 

2200 

5 

2# 

II.  0 

3-24 

0.65 

0.71 

1140 

1.16 

2260 

3 

13-6 

3-99 

0-75 

0.82 

1570 

1.19 

2960 

•X- 

4 

15-3 

4-54 

i.  08 

1.17 

2810 

1.09 

2880 

* 

3>£ 

17.0 

4-95 

i.  06 

1.03 

2890 

1.05 

2920 

*  6 

5^ 

39-0 

11.58 

1-75 

1-57 

10920 

1.27 

8330 

* 

4 

15.6 

4.61 

0.97 

1.  12 

2560 

i-33 

3HO 

*Pencoyd  only. 


(109) 


STE.EL    ZE,E=BARS 

For  Beams,  Girders,  Columns,  or  Truss  Members         TABLE  24 

• 

2 

3 

4 

5 

6 

7 

8 

9        10 

II 

12 

13 

M 

15 

Dimensions 

B 

S 

Beams 

Zee-Bar  Columns 

Practical  Detailing 
Dimensions 

0 

1 
tt 

CO 

"O 

S    . 
O 

tfl 

a 
.2 

lickness  of  Metal 

p 

If 

44 

'Ction-Momer.t 
s  Perpendicular 
to  Web 

dth  of  Web  Plate 

-^•^3 

Radius  ol 
Gyration 

*""  ®  en 

'S,  X 

dius  of  Gyration 
is  Perpendicular 
j  8"  Web  Plate 

Web 

Flango 

s  Coincident 
i  Web  Plate 

s  Perpendic- 
ar  to  Web 

5 

"o 
a 

o 

i 

o 

O 

EH 

^ 

o5  H 

f 

*5 

31 

5 

V 

as 

a 

S 

In. 

Tn.  ; 

Tn. 

Lbs. 

Foot- 

Tn 

Lbs. 

Tn 

Tn 

Lbs. 

Ins. 

Tn 

Tn 

Tn 

In 

3 

X 

Tons 

4.0 

2  1.1 

6-7 

1.28 

6 

3i-9 

1.9 

3.0 

33-6 

1# 

34 

15/8 

3A 

2% 

A 

8.4 

1-58 

40.0 

42.1 

3 

2H 

3/£  ; 

9-7 

1.72 

46.5 

49.0 

3ft 

* 

ii.  4 

1.98 

54-5 

57-5 

3 

2H 

*/t  ; 

12-5 

2.04 

60.2 

63.6 

3A 

2^ 

A 

14.2 

2.28 

68.3 

1-9 

2-9 

72.1 

3-8 

4 

3A 

i/ 

8.2 

2.09 

6^ 

38.3 

2-5 

3-3 

39-6 

4.0 

2 

7A 

2 

u 

4A 

3/8 

T5tf 

10.3 

2.60 

48.1 

49-7 

4X 

3A 

3/8 

12.4 

3-n 

57-9 

59-8 

4 

3A 

A 

13-8 

3-22 

64.9 

67-1 

4A 

3/8 

^ 

3-67 

74-2 

76.8 

A 

17.9 

4.12 

84.0 

86.9 

4 

3A 

5^ 

18.9 

4.03 

89.4 

92.6 

4A 

3/8 

H 

20.9 

4-43 

98.8 

102.3 

3A 

22.9 

4.84 

108.2 

2.6 

3-i 

112.  0 

3-8 

5 

zX 

T6* 

ii.  6 

3-56 

7 

53-8 

31 

3-S 

54-9 

4.0 

2y2 

H 

2*A 

H 

3T5^ 

13-9 

4.26 

64-5 

65.8 

S/s 

3/8 

7 

•16.4 

4.96 

76.0 

77-5 

5 

3* 

^    * 

17-8 

5-12 

83-1 

84.8 

sA 

A 

20.  2 

5-75 

94.2 

96.1 

3/8 

22.6 

6.38 

i°5-3 

107.4 

5 

1% 

n 

23-7 

6.32 

III.  2 

"3-5 

sA 

3  ITS 

26.O 

6.89 

I2I.9 

124-4 

5/8 

3/8 

H 

28.3 

7-47 

132.5 

3.2 

3-3 

135-3 

3-8 

6 

3* 

N 

15.6 

5-63 

7^ 

72.0 

3-7 

3-7 

72.6 

4.0 

3 

7/z 

2% 

y* 

^A 

7 

18.3 

6-55 

84.4 

85,1 

6/s 

3^ 

# 

21.0 

7-48 

96.8 

97.6 

6 

3^2 

A 

22.7 

7.70 

IO5.I 

106.1 

^A 

3r96 

N 

25-4 

8-55 

II7-5 

118.6 

6^ 

3/8 

28.0 

9.40 

129-5 

130.7 

6 

3^ 

«/ 

29-3 

9-36 

136.3 

137.6 

^A 

3A 

8 

32.0 

10.15 

148.7 

150-1 

«jj 

3/8 

34-6 

10.93 

160.7 

3-8 

3-5 

162.2 

3-7 

Section  for  1 
Rivet  Holes 

Lbs.  per  L.  ft. 

Diameter  of 
Rivets 

0 

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WEIGHTS  OF  FLAT  KOLLED  STE,EL  TABLE  25 
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3 

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MMM                                MM                                        04 

112  STRUCTURAL    DESIGNERS'    HANDBOOK. 


CHAPTER  IX.— CAST  IRON  COLUMNS. 

Cast  iron  columns  are  rarely  used  for  very  high  skeleton  con- 
struction. They  should  never  be  so  used  when  there  is  great 
eccentricity  in  the  loading.*  They  are  widely  used  for  buildings  of 
medium  height,  where  outer  bearing  walls  are  provided  or  where 
a  sufficient  distribution  of  substantial  inclosure  and  curtain  walls 
exists  to  brace  the  building  adequately  against  lateral  forces. 

Cast  iron  columns  do  not  lend  themselves  readily  to  the  at- 
tachment of  wind  bracing,  and  because  of  the  loose  connections  of 
the  beams  they  should  seldom  be  used  where  wind  bracing  is  neces- 
sary. 

Different  forms  of  cross  section  are  used  for  cast  iron  columns. 
The  square  section  is  used  a  great  deal  where  the  column  is  to  be 
built  into  a  wall ;  the  round  section  is  generally  used  for  columns 
standing  free  in  a  room ;  and  the  other  form  of  section  the  H  shape 
is  very  popular  for  either  wall  or  free  columns — the  latter  only 
when  it  is  to  be  encased  in  brick  or  plaster  work.  This  section 
has  the  advantage  of  being  open  for  inspection  and  it  is  easy  to 
core.  A  special  section  of  the  same  class — designed  by  the  author 
— is  shown  in  Fig.  20.  It  is  suitable  for  large  size  columns,  in 
fact,  it  is  simply  a  practical  extension  of  the  use  of  the  H  section 
beyond  the  limits  of  the  simple  form.  For  small  posts  or  struts 
such  as  stair  posts  and  the  like,  the  star  section  (Fig.  23)  is  some- 
times used. 

IN  THE.  DESIGN  OF  A  CAST  IRON  COLUMN  three  steps  are 
taken:  first,  the  ratio  of  slenderness  is  fixed  within  certain  limits; 
second,  the  area  of  the  section  is  found;  and  third  the  section  is 
designed. 

The  first  step  has  already  been  described  in  Chapter  VII  and 
the  Diagrams  Nos.  30  and  32  (as  well  as  Diagram  No.  34)  found 
in  that  chapter  will  be  used  in  conjunction  with  the  diagrams  in 
this  chapter. 

The  second  and  third  steps  will  be  fully  explained  in  the  de- 
scriptions of  Diagrams  Nos.  35  and  36. 

Diagram  No.  35  is  based  on  the  provisions  for  allowable 
stresses  contained  in  the  "Code"  (N.  Y.  C).  Diagram  No.  36 

*Small  eccentricities  of  loading  are  sometimes  allowed  by  increasing  the 
area  of  the  section  enough  to  take  care  of  the  bending  stress  due  to  the  ec- 
centricity. 


CAST  IRON    COLUMNS.  113 

embodies  what  the  author  considers  to  be  more  conservative 
values*  for  use  in  general  practice.  For  a  column  ratio  of  10 
the  allowed  stress  is  just  the  same  as  for  the  preceding  diagram, 
but  the  reduction  of  stress  with  increasing1  ratio  of  slenderness  is 
much  greater  than  that  provided  by  the  "Code." 

DIAGRAMS  NOS.  35  AND  36:— The  construction  of  these  dia- 
grams is  similar  to  that  of  No.  33  for  steel  columns.  Abscissas 
represent  column  ratios,  ordinates  represent  areas  and  the  loads 
are  represented  by  the  curves  on  the  diagram.  A  supplementary 
ordinate  scale  at  the  right  of  these  diagrams  also  gives  the  weight 
per  lineal  foot  for  any  area  of  cross  section.  This  value  is  given 
in  the  tables  following  these  diagrams  in  preference  to  the  area  of 
the  section  because  of  its  double  value  for  both  design  and  esti- 
mates. 

An  example  will  best  illustrate  the  application  of  diagrams  to 
the  design  of  cast  iron  columns  loaded  with  concentric  and  eccen- 
tric loads. 

Example: — A  column  10  ft.  long  has  a  load  of  75  tons,  8  tons  of  which 
is  located  6  in.  from  the  neutral  axis  perpendicular  to  the  web.  The  column 
section  is  the  H  as  shown  in  Fig.  19  and  is  assumed  to  be  10  ins.  square. 

Solution: — The  center  of  gravity  of  the  combined  concentric  and  ec- 
centric load  is  0.64  in.  from  the  neutral  axis  perpendicular  to  the  web.  The 
coefficient  of  eccentricity  is  5  times  0.64  or  3.2.  The  radius  of  gyration  is 
4  ins.  about  the  axis  perpendicular  to  the  web,  in  which  case  the  area  re- 
quired for  this  eccentricity  is  20%  of  what  would  be  required  for  the  same 
load  concentrically  located,  thus  for  the  above  load  eccentrically  located  an 
equivalent  concentric  load  is  120%  of  75  or  90  tons. 

On  Diagram  No.  36  the  area  required  for  a  load  of  9.0  tons  on 
a  column  with  a  ratio  of  slenderness  of  50  is  3.15  sq.  ins.,  therefore, 
for  a  column  load  of  90  tons  the  area  would  be  31.5  sq.  ins.  This 
same  diagram  gives  the  weight  per  lineal  foot  of  column  section 
for  the  above  load  as  98.5  pounds. 

According  to  Table  No.  26  a  10  x  10  column  ij  in.  metal  is  the 
nearest  to  this  requirement. 

The  reader  is  referred  to  a  valuable  discussion  on  the  strength  of  cast 
iron  columns  in  "Kent's  Mechanical  Engineer's  Pocket  Book,"  pp.  250-252. 


114 


STRUCTURAL    DESIGNERS'    HANDBOOK: 


Diagram  No.  35 

For  giving  the  safe  loads  on  cast-iron  columns  as  specified 
by  the  New  York  Building  Code. 


\£> 


u 


5 


20 


.10  -40  70 

RATIO  OF  SLENDERNESS 


Diagram  No.  36 

For  giving  the  safe  loads  on  cast-iron  columns  as  recommended 
by  the  author. 


RATIO  OF  SLENDERNESS 
U15) 


n6 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


CAST    IRON    COLUMN    SECTIONS 


H 


Fig.  19 


WEIGHT    IN   POUNDS 
PER  FOOT 


Size 

Thickness  of  Metal 
Table  No.  26 

£ 

X 

1 

1* 

IX 

IK 

2 

5*    5* 
6x6 
6x    8 
7x    7 
7x    9 
8x    8 
8  x  10 
9x9 
9  x  10 

10  X  10 
10  X  12 
12  X  12 

21.8 

26.5 

g! 

43-4 
45-5 

40.6 

499 
56.2 

59-3 
65.6 
68.6 
75-o 
78.0 
81.2 
87-5 
93-6 
106.0 

48.6 
60.5 
64.8 
72.0 
80.2 
84.0 
91.6 
95-5 
96.4 
108.0 
115  o 
130.0 

84.2 

895 
98.2 
107.8 

112.  0 
II7.0 
126.0 
136.0 
155-0 

155-8 
177-8 

175-0 
200.  o 

52.7 

59-8 

*  Second  dimension  is  in  direction  of  web. 


Fig.  20 


WEIGHT    IN   POUNDS 
PEE  FOOT 


Size 

Thickness  of  Metal 
Table  No.  27 

1 

IK 

IK 

1% 

2 

2X 

2K 

2K 

3 

12  X  16* 
20 

24 
16  x  16 
20 
24 

20  X  20 

24 
28 
24X24 
28 

24  x  28 

1  60 
172 
185 
197 
2IO 
222 

199 
214 
230 

2J5 
261 
276 

237 
256 
275 
293 
312 

33i 

369 
388 
407 

443 
462 
490 

275 
297 

319 
34i 

363 
385 
428 

450 

472 

515 

537 
575 

3J3 

338 
363 
388 

4i3 
438 
487 
5i2 

III 

613 

663 

434 

462 
490 
547 
575 
603 
660 
688 
753 

606 

637 
669 

725 
762 
840 

734 
802 
836 
93i 

798 

873 
910 
1023 

*  Second  dimension  is  in  direction  of  web. 


O 


CAST   IRON    COLUMNS. 


CAST    IRON    COLUMN    SECTIONS 


117 


Fig.  21 


WEIGHT    IN    POUNDS 
PER    FOOT 


Outside 
Diameter 

Thickness  of  Metal 
Table  28 

X 

1 

IK 

1* 

IX 

2 

2* 

2X 

2M 

3 

I 

8 

9 
10 
ii 

12 
13 
H 

n 

18 

20 

31.2 
38.6 
45-9 
53-3 
60.6 

39-i 
490 
58.8 
68.6 
78.4 
88  2 
98.0 
107.8 

58.2 

70.5 
82.7 

95-o 
107.2 

II9-5 
I3I-7 
1440 
156.2 
168.5 

100.3 
125.0 
139-7 
154-4 
169.0 
189.0 
198.5 

213-3 
243.0 

I4L5 

158.7 
175-8 
193.0 

210.0 

227.5 

2445 
279.0 
3I3-0 

196.0 
215-5 
235-5 
255-0 
275-0 
314.0 
253-0 

281.5 
303-0 
348.0 
392.0 

331-0 
380.0 
429.0 

411.0 

465.0 

441-0 
500.0 



D 


rig.  22 


WEIGHT  IN  POUNDS 
PEE  FOOT 


Size 

Thickness  of  Metal 
Table  29 

X 

1 

2& 

IX 

IX 

2 

2# 

2K 

2% 

3 

6x    6 

49 

63 

74 

8 

59 

75 

90 

10 

68 

88 

105 

12 

77 

100 

121 

16 

96 

125 

152 

8x8 

68 

88 

105 

10 

77 

IOO 

121 

12 

87 

112 

137 

16 

105 

137 

1  68 

IO  X  IO 

87 

112 

137 

159 

12 

96 

125 

152 

178 

16 

H5 

!50 

183 

215 

12  X  12 

1^7 

1  68 

J97 

224 

250 

l6 

162 

199 

234 

268 

300 

16  x  16 

187 

230 

272 

311 

35° 

386 

20 

261 

TOO 

7CC 

400 

442 

24 

^46 

7QQ 

4"?o 

499 

546 

20  x  20 

^46 

7  OQ 

4CJO 

499 

^46 

24 

•384 

442 

499 

ccc 

609 

24  x  24 

421 

486 

549 

611 

671 

730 

787 

STRUCTURAL    DESIGNERS'    HANDBOOK. 


CAST    IRON    COLUMN    SECTIONS 

WEIGHT    IN    POUNDS 
Fig.  23  PER    FOOT 


Thickness  of  Metal 

Size 

Table  30 

% 

* 

% 

K 

X 

1 

3"x3" 

6.6 

8.6 

10.5 

12.4 

4x4 

9.0 

11.7 

14.4 

17.0 

5   *5 

14.9 

18.3 

21.7 

25.0 

28.1 

6x6 

18.0 

22.3 

26.4 

3°-  4 

34-4 

CAST    IRON    GAS    PIPE, 

WEIGHT    IN    POUNDS 
PER    FOOT 


Size 

Thickness  of  Metal 
Table  31 

% 

K 

T7B 

y 

1A 
39.36 

& 
54-o 

2"<p 

3" 
4" 
5" 
6" 
8" 
10" 

6.96 

ii.  16 

15.84 

21.00 

26.64 

Part  IV.     Miscellaneous. 

CHAPTER  X.    LOADS. 

Before  the  framework  of  a  building  can  be  designed,  the  ex- 
ternal forces  which  act  on  the  structure,  i.  e.,  the  loads,  must  be 
known  or  assumed.  In  this  chapter  are  given  some  average  values 
which  may  be  used  for  the  different  items  in  estimating  loads,  to- 
gether with  the  principal  provisions  regarding  loading  which  are 
found  in  the  "Code"  (N.  Y.  C). 

Loads  are  usually  divided  into  Dead  Loads,  Live  Loads  and 
Wind  Loads.  Sometimes  wind  loads  are  included  under  live 
loads. 

DEAD  LOADS. 

THE  DEAD  LOADS  CARRIED  BY  FLOOR  GIRDERS  consist  of . 
the  steel  beams,  connection  angles,  tie  rods  and  other  fittings ; 
floor  arches,  nailing  strips,  filling  and  finished  flooring;  partitions, 
stairs  and  other  permanent  construction ;  and  suspended  ceilings, 
pipes  and  conduits. 

THE  DEAD  LOADS  CARRIED  BY  COLUMNS  consist  of:  the 
dead  loads  from  the  floor  or  floors  supported  by  the  column ;  the 
column  itself,  including  the  metal  and  covering  material;  all  pipes 
and  conduits  suspended  to  the  column ;  and  loads  from  trusses  or 
girders  carrying  brick  walls,  vaults  or  other  permanent  loads. 

THE  WEIGHT  OF  STEEL  FLOOR  FRAMING  may  be  deter- 
mined approximately  from  the  two  accompanying  Diagrams  Nos. 
37  and  38.  Diagram  No.  37  applies  to  floors  intended  to  carry  a 
total  load  (live  and  dead)  of  about  150  lbs.tper  sq.  ft.  Diagram 
No.  38  applies  to  floors  intended  to  carry  a  total  load  of  about 
300  Ibs.  per  sq.  ft.  In  these  diagrams  abscissas  represent  span  in 
feet,  and  ordinates  represent  weight  of  steel  per  square  foot  of 
floor.  Two  sets  of  lines  are  drawn  on  each  diagram :  the  upper 
set  consisting  of  three  lines  is  for  floor  beams  spaced  3,  4  or  5  ft. ; 
the  lower  five  lines  are  for  floor  girders,  representing  spacings  of 
10,  15,  20,25  and  30  ft. 

To  use  either  of  the  two  diagrams,  take  an  abscissa  equal  to 

(119) 


Diagram  No*  37 

For  giving  the  weight  of  steel  required  in  floors  where  the 
loads  are  a  minimum. 

SPAN   OF    BEAMS   IN    FEET   OR   SPAN    OF   GIRDERS  IN  FEET. 
10  19  20  25  30 


N 


P£R. 


FOOT 
4-  i^c. 


f  otz 


<r 


*•/ 


t 


4V 


7 


nt 


/ 


N 


APPKOVlMfVTC 


~~-  — 

0* 

.Of 

;M 

-(• 

TV 

Of 

•A 

Iff 

^ 

L 

e 

5- 

"^•^^ 

^ 

^ 

/ 

\ 

*--  —  „ 

"~  — 

/ 

^^^ 

^~ 

~~». 

^ 

^ 

r= 

=H 

^ 

=  = 

10  15  20  25          30 

SPAN   OF   BEAMS   IN   FEET  OR  SPAN   OF  GIRDERS  IN  FEET 

(120) 


LOADS. 

Diagram  No.  38 


121 


For  giving  the  weight  of  steel  required  in  floors  where  the 
loads  are  a  maximum. 

SPAN   OF    BEAMS   IN    FEET   OR  SPAN    OF  GIRDERS  IN   FEET 

10  15  20  "25         20 

O 


§    N 
O 


u_    \0 

O 

s 

o    « 

LL      O\ 

LU 
tt 
< 

^ 

8  ^ 

be 

LU 
O. 


•?OT 


COfCEC'    Of4 


oep-c? 


/ 


2 


<x 


N  o 


|0  15  i       20  25         3o 

SPAN    OF    BEAMS    IN    FEET    OR   SPAN    OF  GIRDERS   IN    FEET 


122 


STRUCTURAL    DESIGNERS'     HANDBOOK'. 


Diagram  No*  39 

For  giving  the  weight  of  joists  per  square  foot  of  floor. 
DEPTH  OF  JOIST 

e"        a"        10"       12"       14"       16" 


JOJE-I5- 


9- 


E-12-r 


7EE 


5. 


Y.R 

w.o. 


-14- 


9--I2- 


^10^ 


--6—8- 


3- 


^=32  =  4^ 


r.p 

W.O 


6" 


10"          12"          14" 

DEPTH  OF  JOIST 


16" 


LOADS.  123 

the  span  of  the  floor  beams  in  feet  and  follow  up  to  the  diagonal 
representing  the  assumed  spacing  of  the  beams  in  feet.  The  hori- 
zontal at  the  intersection  gives  the  weight  of  floor  beams  in  pounds 
per  square  foot  of  floor.  Then  take  an  abscissa  equal  to  the  span 
of  the  girders  and  follow  to  the  diagonal  representing  the  spacing 
— the  horizontal  at  the  intersection  gives  the  weight  of  the  girders 
per  square  foot  of  floor.  The  sum  of  the  weights  of  the  beams  and 
the  girders  gives  the  total  weight  of  steel  per  square  foot  of  floor. 
At  the  bottom  of  Diagram  No.  37  are  two  curves  which  represent  ap- 
proximately the  limiting  weights  of  connection  angles  per  square  foot  of 
floor  for  different  spans  of  beam.  Evidently  these  weights  are  too  small 
to  affect  the  loading. 

THE  WEIGHT  OF  WOODEN  FLOOR  BEAMS  may  be  deter- 
mined approximately  from  Diagram  No.  39  herewith.  In  this  dia- 
gram abscissas  represent  depth  of  the  beam  and  ordinates  represent 
"  weight  per  square  foot  of  floor.  The  diagonal  lines  on  the  diagram 
represent  different  breadths  of  beam,  and  different  spacing  of 
beams.  The  ordinates  may  be  measured  on  one  of  three  scales  at 
the  right  of  the  diagram :  these  scales  give  the  weights  per  square 
foot  of  floor  respectively  for  white  pine,  spruce  and  yellow  pine 
or  white  oak. 

FLOOR  ARCHES: — The  weight  of  tile  arches  varies  from  18 
to  40  Ibs,  per  sq.  ft.  according  to  the  depth,  density  of  tile,  thick- 
ness, and  distance  of  webs  apart.  About  5  IDS.  per  sq.  ft.  should 
be  added  to  the  weight  of  floor  arches  for  the  mortar  in  the  joints. 
The  weight  of  concrete  arches  varies  from  18  to  40  Ibs.  per  sq.  ft. 
according  to  the  span  of  the  arch  and  to  the  system  of  construc- 
tion* adopted.  ,. 

FLOORING  MATERIAL: — Hardwood  floors  weigh  about  4 
Ibs.  per  sq.  ft.,  for  every  inch  in  thickness,  and  softwood  about  3 
Ibs.  Nailing  strips  weigh  about  2  Ibs.  per  sq.  ft.  of  floor.  Tile  or 
terrazza  floors  weigh  about  14  Ibs.  per  sq.  ft.  for  every  inch  in 
thickness. 

Concrete  filling  weighs  from  6  to  8  Ibs.  per  sq.  ft.  for  every 
inch  in  thickness  according  to  composition. 

Plastered  ceilings  weigh  about  8  Ibs.  per  sq.  ft.  In  case  of  sus- 
pended ceilings,  the  weight  of  the  steel  work  and  tile  or  lath  must 
be  added. 


*Valuable  information  on  the  various  flooring  systems  will  be  found  in 
Frietag's  "Architectural  Engineering"  and  Kidder's  "Building  Construction 
and  Superintendence,"  Part  I. 


124  STRUCTURAL    DESIGNERS'    HANDBOOK. 

PARTITIONS: — Tile  plastered  on  both  sides  weighs  from  24 
to  40  Ibs.  per  sq.  ft.  of  wall  surface.  Expanded  metal  weighs  from 
18  to  22  Ibs.  per  sq.  ft. 

BRICK  WALLS: — The  weight  of  walls  will  be  found  on  Dia- 
gram No.  40  in  Chapter  XII. 

LIVE  LOADS. 

Live  or  variable  loads  consist  of  all  loads  other  than  dead 
loads.  The  "Code"  (N.  Y.  C.)  provides  that  :— 

"Every  floor  shall  be  of  sufficient  strength  to  bear  safely  the  weight  to 
be  imposed  thereon  in  addition  to  the  weight  of  the  materials  of  which  the 
floor  is  composed.  Thus: — 

Floor  Loads  per  sq.   ft. 

Dwelling  house   60  Ibs. 

Apartment  house  60  " 

Tenement  house  60  " 

Hotel  or  lodging  house    60  " 

Office  buildings: 

Above  ist  floor 75  " 

ist  floor   150  " 

School  or  place  of  instruction    75  " 

Stable  or  carriage  house    75  " 

Place  of  public  assembly    90  " 

Ordinary  stores,  light  manufacturing  and  light  storage.  .120  " 
Store  where  heavy  materials  are  kept,  warehouse  or  fac- 
tory  150  " 

Roofs  pitch  less  than  20°   50  " 

pitch  more  than  20°    30  " 

(load  on  a  horizontal  plane.) 

Sidewalks  between  the  curb  and  area  lines 300  " 

"For  the  purpose  of  determining  the  carrying  capacity  of  columns  in 
dwellings,  office  buildings,  stores,  stables  and  public  buildings  when  over 
five  stories  in  height,  a  reduction  of  the  live  loads  shall  be  permissible  as 
follows: 

"For  the  roof  and  top  floor  the  full  live  loads  shall  be  used;  for  each 
succeeding  lower  floor  it  shall  be  permissible  to  reduce  the  live  load  by  5% 
until  50%  of  the  live  loads  fixed  by  this  section  is  reached,  when  such  re- 
duced loads  shall  be  used  for  all  remaining  floors." 

The  strength  of  factory  floors,  intended  to  carry  running  ma- 
chinery should  be  increased  about  50%  above  the  preceding  pro- 
visions. 

Regarding  the  reduction  of  live  loads  on  columns,  as  speci- 
fied in  the  above  quotation,  it  may  be  remarked  that  this  does  not 


LOADS.  125 

take  into  account  the  area  of  floor  tributary  to  the  column  as  af- 
fecting the  allowable  percentage  of  reduction — a  rational  provision 
should  allow  for  this. 

LIVE  LOADS  ON  FOOTINGS :— According  to  the  "Code"  (N. 
Y.  C.)  the  loads  exerting  pressure  under  the  footings  of  founda- 
tions in  buildings  more  than  three  stories  in  height  are  to  be  com- 
puted as  follows : 

"For  warehouses  and  factories  they  are  to  be  the  full  dead  and  the  full 
live  load.  In  stores  and  buildings  for  light  manufacturing  purposes  they  are 
to  be  the  full  dead  load  and  75%  of  the  live  load.  In  churches,  school  houses 
and  places  of  public  amusement,  they  are  to  be  the  full  dead  load  and  75% 
of  the  live  load.  In  office  buildings,  hotels,  dwellings,  apartment  houses, 
tenement  houses,  lodging  houses  and  stables,  they  are  to  be  the  full  dead 
load  and  60%  of  the  live  load.  Footings  shall  be  so  designed  that  the  loads 
will  be  as  nearly  uniform  as  possible  and  not  in  excess  of  the  safe  bearing 
capacity  of  the  soil." 

WIND  PRESSURE  ON  BUILDINGS :— The  wind  pressure  al- 
lowed for  on  buildings  is  very  much  a  matter  of  guess  work.  The 
provisions  of  the  "Code"  (N.  Y.  C.)  however,  are  recognized  as  rep- 
resenting safe  limits.  These  provide  that: 

"All  structures  exposed  to  wind  shall  be  designed  to  resist  a  horizontal 
wind  pressure  of  30  Ibs.  for  every  sq.  ft.  of  surface  thus  exposed,  from  the 
ground  to  the  top  of  same  including  roof,  in  any  direction.  In  no  case  shall 
the  over-turning  moment  due  to  wind  pressure  exceed  75%  of  the  moment 
of  stability  of  the  structure.  In  all  structures  exposed  to  wind,  if  the  resist- 
ing moments  of  the  ordinary  materials  of  construction,  such  as  masonry, 
partitions,  floors  and  connections,  are  not  sufficient  to  resist  the  moment  of 
distortion  due  to  wind  pressure,  taken  in  any  direction  on  any  part  of  the 
structure,  additional  bracing  shall  be  introduced  sufficient  to  make  up  the 
difference  in  moments.  In  calculations  for  wind  bracing,  the  working 
stresses  set  forth  in  this  code  may  be  increased  by  50%.  In  buildings  under 
100  ft.  in  height,  provided  the  height  does  not  exceed  four  times  the  average 
width  of  the  base,  the  wind  pressure  may  be  disregarded." 


126 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


CHAPTER  XL     UNIT  STRESSES. 

The  allowable  working  stresses  to  be  used  in  designing  are  of 
fundamental  importance.  In  the  construction  of  the  diagrams 
and  tables  throughout  this  book  the  following  stresses  were  con- 
sidered. As  previously  stated  these  stresses  were  taken  from  the 
"Code"  (N.  Y.  C.)  and  because  of  their  importance  they  are  col- 
lected together  in  this  Chapter  for  general  use  and  reference. 

SAFE  LOAD  ON  MASONRY  WORK.— The  safe  bearing  load  in  tons 
per  superficial  foot  shall  be  taken  at 
8  for  brickwork  in  lime  mortar, 
iil/2  for  brickwork  lime  and  cement  mixed, 
15  for  brickwork  cement  mortar 

rubble-stone  work  in  Portland  cement  mortar 

"      cement  mortar 
"  "       lime  and  cement 

"       lime  mortar 
Portland  cement  concrete 
cement  concrete   (natural) 

STRENGTH  OF  COLUMNS:— In  columns  or  compression  members 
with  flat  ends  of  cast  iron,  steel,  wrought  iron  or  wood,  the  stress  per  square 
inch  shall  not  exceed  that  given  in  the  following  tables: 

Working  stresses  per  square  inch 
of  section. 


10 

8 
7 
5 
15 
8 


When  the  length  divided  by  least 
radius  of  gyration  equals 


120 

no 

100 

90 

80 
70 
6p 
50 
40 
30 

20 
IO 


Cast  iron. 

Wrought 
Steel.            iron. 
8,240              4,400 
8,820              5,200 
9,400             6,000 
9,980             6,800 
10,560              7,600 
11,140             8,400 
11,720             9,200 
12,300            10,000 
12,880            10,800 
13,460            1  1,  600 
14,040            12,400 
14,620            13,200 

stresses  per  square 
i  of  section. 



9,200 
9,500 

9,800 

10,100 

10,400 
:o,7oo 

11,000 

Working 
incl 

When  the  length  divided  by  the  least 
diameter  equals 


'- 

20 

15 

12 
10 


Long        White  pine, 

leaf  yel-         Norway 

low  pine,  pine,  Spruce  Oak. 
460  350  390 
550  425  475 
640  500  560 


730 
784 
820 


575 
620 
650 


696 
730 


UNIT 


127 


And  in  like  proportion  for  intermediate  ratios.  Five-eighths  the  values 
given  for  white  pine  shall  apply  to  chestnut  and  hemlock  posts.  For  locust 
posts  use  il/2  the  value  given  for  white  pine. 

Columns  and  compression  members  shall  not  be  used  having  an  unsup- 
ported length  of  greater  ratios  than  given  in  the  tables. 

WORKING  STRESSES:— The  safe  carrying  capacity  of  the  various 
materials  of  construction  (except  in  the  case  of  columns)  shall  be  deter- 
mined by  the  following  working  stresses  in  pounds  per  square  inch  of  sec- 
tion area: 


COMPRESSION    (DIRECT). 


Rolled  steel   16,000 

Cast  steel   16,000 

Wrought  iron I2,COD 

Cast  iron  (in  short  blocks) .  16,003 
Steel  pins  and  rivets   (bear- 
ing)      20,000 

Wrought  iron  pins  and  rivets 

(bearing)    I5,oco 


With  Across 

grain,  grain.* 

Oak   900  500 

Yellow  pine   1,000  350 

White  pine  800  200 

Spruce   800  200 

Locust   1,200 

Hemlock    500  150 

Chestnut    500  250 


Concrete  (Portland)  cement,  I ;  sand,  2;  stone,  4 230 

Concrete  (Portland;  cement,  i;  sand,  2;  stone,  5 208 

Concrete,  Rosendale,  or  equal,  cement,  i;  sand,  2;  stone,  4..  125 

Concrete,  Rosendale,  or  equal,  cement,  i;  sand,  2;  stone,  5..  in 

Rubble  stonework  in  Portland  cement  mortar 140 

Rubble  stonework  in  Rosendale  cement  mortar HI 

Rubble  stonework  in  lime  and  cement  mortar 97 

Rubble  stonework  in  lime  mortar 7° 

Brickwork  in  Portland  cement  mortar;  cement,  i;  sand,  3.  ...  250 
Brickwork  in  Rosendale,  or  equal,  cement  mortar;  cement,  i; 

sand,  3 208 

Brickwork  in  lime  and  cement  mortar;  cement,  i;  lime,  i; 

sand,  6 160 

Brickwork  in  lime  mortar;  lime,  i ;  sand,  4 in 

Granites  (according  to  test) 1,000  to  2,400 

Greenwich  stone  1,200 

Gneiss  (New  York  City) 1,300 

Limestones  (according  to  test) 700  to  2,300 

Marbles  (according  to  test) 600  to  1,200 

Sandstones  (according  to  test) 400  to  1,600 

Bluestone,  North  River 2,000 

Brick  (Haverstraw,  flatwise) 300 

Slate  1,000 


*These  values  for  compression  across  the  grain  have  been  revised  by 
the  author. 


128  STRUCTURAL    DESIGNERS'    HANDBOOK. 

TENSION   (DIRECT). 

Rolled  steel   16,000  White  pine  800 

Cast  steel    16,000  Spruce   800 

Wrought  iron   12,000  Oak   1,000 

Cast  iron    3,ooo  Hemlock  600 

Yellow  pine  1,200 

SHEAR. 

Steel  web  plates 9,000  With  Across 

Steel  shop  rivets  and  pins..  10,000  fiber.  fiber. 

Steel  field  rivets 8,000        Yellow  pine    70  500 

Steel   field  bolts 7,000       White  pine   40  250 

Wrought  iron  web  plates. ..  6,000        Spruce    50  320- 

Wrought    iron    shop    rivets                      Oak    100  600 

and  pins    7,5oo       Locust 100  720 

Wrought  iron  field  rivets..  6,000        Hemlock 40  275 

Wrought  iron  field  bolts...  5,500  Chestnut 150 

Cast   iron   3,000 

SAFE  EXTREME  FIBER  STRESS  (BENDING). 

Rolled  steel  beams. 16,000        Granite    180 

Rolled  steel  pins,  rivets  and                      Greenwich   stone    15° 

bolts   20,000        Gneiss   (New  York  *City) 150 

Riveted     steel     beams      (net                      Limestone    15° 

flange   section)    14,000        Slate    400 

Rolled  wrought-iron  beams.  12,000        Marble    120 

Rolled     wrought-iron     pins,                     Sandstone    100 

rivets  and  bolts 15,000        Blue  stone,  North  River 300 

Riveted  wrought-iron   beams 

(net  flange   section) 12,000  Concrete     (Portland)     cement, 

Cast-iron,  compression  side.  16,000           i;  sand,  2;  stone,  4 30 

Cast-iron,  tension  side 3,ooo  Concrete     (Portland)     cement, 

Yellow   pine    i ,200           I ;  sand,  2 ;  stone,  5 20 

White   pine    800  Concrete  (Rosendale,or  equal) 

Spruce    800  cement,  i ;  sand,  2;  stone,  4. .  16 

Oak    1,000  Concrete  (Rosendale,  or  equal) 

Locust    1,200  cement,  i ;  sand,  2;  stone,  5. .  10 

Hemlock   600        Brick  (common)    50 

Chestnut    800        Brickwork  (in  cement) 30 

BEARING  CAPACITY  OF  SOIL.— Where  no  test  of  the  sustaining 
power  of  the  soil  is  made,  different  soils,  excluding  mud,  at  the  bottom  of 
footings  shall  be  deemed  to  safely  sustain  the  following  loads  in  tons  per 
superficial  foot,  namely: 

Soft   clay    i. 

Ordinary  clay  and  sand  together,  in  layers,  wet  and  springy 2. 

Loam,   clay   or  fine   sand,   firm  and   dry 3. 

Very  firm,  coarse  sand,  stiff  gravel  or  hard  clay 4. 

"When  a  doubt  arises  as  to  the  safe  sustaining  power  of  earth  upon 
which  a  building  is  to  be  erected,  the  Department  of  Buildings  may  order 
borings  to  be  made,  or  direct  the  sustaining  power  of  the  soil  to  be  tested 
by  and  at  the  expense  of  the  owner  of  the  proposed  building." 


BRICK    WALLS.  I2Q 


CHAPTER  XII.     BRICK  WALLS. 

The  walls  of  a  building  are  an  important  part  of  the  loads  in 
the  case  of  skeleton  construction.  In  the  case  of  building  where 
the  walls  are  the  principal  supporting  element  the  strength,  thick- 
ness, etc.,  of  the  walls  are  essential  items  in  their  design.  In  many 
cities  the  building  laws  prescribe  the  thickness  for  the  various  con- 
ditions in  the  construction  of  walls.  An  especially  full  set  of  provi- 
sions of  this  nature  is  contained  in  the  "Code"  (N.  Y.  C.)  and  they 
are  taken  as  a  basis  for  this  chapter.  These  provisions  divide  the 
walls  of  buildings  into  three  classes :  walls  for  dwelling  houses, 
walls  for  warehouses  and  inclosure  walls  for  skeleton  structures. 

WALLS  FOR  DWELLING  HOUSES.— This  class  includes  the  fol- 
lowing buildings: 

Apartment  Houses,  Hotels, 

Asylums,  Laboratories, 

Club  Houses,  Lodging  Houses, 

Convents,  Parish  Buildings, 

Dormitories,  Schools, 

Dwellings,  Studios, 

Hospitals,  Tenements. 

WALLS  FOR  WAREHOUSES.— This  class  includes    the     following 
buildings: 

Armories,  Observatories, 

Breweries,  Office   Buildings, 

Churches,  Police  Stations, 

Cooperage  Shops,  Printing  Houses, 

Court  Houses,  P'ublic  Assembly  Buildings, 

Factories,  Pumping  -Stations, 

Foundries,  Railroad  Buildings, 

Jails,  Slaughter   Houses, 

Libraries,  Stables, 

Light  and  Power  Houses,  Stores, 

Machine  Shops,  Theatres, 

Markets,  Warehouses, 

Mills,  Wheelwright  Shops. 

Museums, 

TNCLOSURE  WALLS  FOR   SKELETON  STRUCTURES.— These 

are  walls  of  brick  built  in  between  iron  or  steel  columns,   and  supported 
wholly  or  in  part  on  iron  or  steel  girders. 

THICKNESS  AND  WEIGHT  OF  WALLS. 

The  provisions  of  the  "Code"  for  thicknesses  of  these  three 
classes  of  walls  have  been  embodied  in  a  single  diagram. 

DIAGRAM  NO.  40  (GIVING  THICKNESS  AND  WEIGHT  OF 
WALLS) : — In  each  of  the  foregoing  classes  of  walls  the  thickness 


130  STRUCTURAL    DESIGNERS'    HANDBOOK. 

varies  with  the  height  above  the  curb  level.  These  variations  are 
represented  in  five  sections  on  this  diagram.  In  each  section  the 
full  unshaded  outline  represents  "warehouse  walls,"  the  dotted  line 
represents  "dwelling  house  walls,  and  the  full  shaded  portion  repre- 
sents "inclosure  walls  for  skeleton  structures."  The  thicknesses 
for  each  case  are  indicated  by  vertical  lines,  each  space  of  which 
represents  a  thickness  equal  to  one  half  the  length  of  a  brick  or 
about  4  ins.  On  three  of  these  sections  is  given  the  weight  of  wall 
per  lineal  foot  for  the  different  vertical  heights  at  which  the  figures 
for  the  weights  are  placed.  These  weights  apply  to  "warehouse 
walls."  A  supplementary  scale  at  the  right  of  the  diagram  gives  the 
weight  per  lineal  foot  of  skeleton  inclosure  walls  for  different 
heights  below  the  top.  A  farther  ordinate  scale,  at  the  extreme 
right,  gives  the  number  of  bricks  in  such  skeleton  walls,  per  lineal 
foot  of  wall. 

Three  supplementary  scales  at  the  left  of  the  diagram  will  be 
found  useful.    They  show: — 

(1)  Number  of  stories,  at  different  levels,  if  stories  are  10  ft. 
from  floor  to  floor. 

(2)  The  same  if  stories  are  \2\  ft.  from  floor  to  floor. 

(3)  The  floor  area  gained,  per  lineal  foot  of  wall,  by  using 
skeleton  walls  instead  of  warehouse  walls ;  this  latter  is  for  the  ac- 
cumulated gain  for  all  the  floors — the  floors  are  assumed  to  be 
12^  ft.  apart  vertically. 

CONDITIONS  THAT  WILL  MODIFY  THE  FOREGOING  PRO- 
VISIONS.—"If  there  is  a  clear  span  of  over  25  ft.  between  the  bearing: 
walls*  of  warehouses  (26  ft.  for  dwelling  houses),  such  walls  shall  be  4  ins. 
more  in  thickness  than  in  this  section  specified,  for  every  12^  ft.  or  fraction 
thereof,  that  said  walls  are  more  than  25  ft.  apart  (26  ft.  for  dwellings),  or 
shall  have,  instead  of  the  increased  thickness,  piers  or  buttresses." 

"All  buildings,  not  excepting  dwellings,  that  are  over  105  ft.  in  depth, 
without  a  cross  wall  or  proper  piers  or  buttresses,  shall  have  the  side  or 
bearing  walls  increased  in  thickness  4  ins.  more  than  is  specified  in  the 
respective  sections  of  this  code  for  the  thickness  of  walls,  for  every  ic$ 
ft.,  or  part  thereof,  that  the  said  buildings  are  over  105  ft.  in  depth." 

"If  any  horizontal  section  through  any  part  of  any  bearing  wall  in  any 
building  shows  more  than  30%  area  of  flues  and  openings,  the  said  wall 
shall  be  increased  4  ins.  in  thickness  for  every  15%  or  fraction  thereof,  of 
flue  or  opening  area  in  excess  of  30%." 

"Non-bearing  walls  may  be  4  ins.  less  in  thickness,  provided  none  are 
less  than  12  ins.,  for  warehouses  and  dwellings." 

^Bearing  walls  are  those  walls  on  which  beams,  girders  or  trusses  rest. 


BRICK:  WALLS.  131 

FOUNDATION  WALLS. 

"When  either  bearing  or  skeleton  walls  are  supported,  the  foundation 
walls,  if  built  of  rubble-stone  or  Portland  cement  concrete,  shall  be  at 
least  8  ins.  thicker  than  the  wall  next  above  them,  to  a  depth  of  12  ft.  below 
the  curb  level;  and  for  every  additional  10  ft.,  or  part  thereof,  deeper,  they 
shall  be  increased  4  ins.  in  thickness.  If  built  of  brick,  they  shall  be  at  least 
4  ins.  thicker  than  the  wall  next  above  them  to  a  depth  of  12  ft.  below  the 
curb  level;  and  for  every  additional  10  ft.  or  part  thereof,  deeper,  they 
shall  be  increased  4  ins.  in  thickness.  The  footing  or  base  course  shall  be 
of  stone  or  of  concrete,  or  both,  or  of  concrete  and  stepped-up  brickwork, 
of  sufficient  thickness  and  area  to  safely  bear  the  weight  to  be  imposed 
thereon." 

"The  thickness  of  a  RETAINING  WALL  at  its  base  shall  be  in  no 
case  less  than  one-fourth  of  its  height." 

BRICK  WALLS  FOR  SKELETON  CONSTRUCTION. 

"Where  columns  are  used  to  support  iron  or  steel  girders  carrying  in- 
closure  walls,  the  said  columns  shall  on  their  exposed  outer  and  inner  sur- 
faces be  constructed  to  resist  fire  by  having  a  casing  of  brickwork  not  less 
than  8  ins.  in  thickness  on  the  outer  surfaces,  nor  less  than  4  ins.  on  the 
inner  surfaces,  and  all  bonded  into  the  brickwork  of  the  inclosure  walls. 

"The  exposed  sides  of  the  iron  or  steel  girders  shall  be  similarly  cov- 
ered in  with  brickwork  not  less  than  4  ins.  in  thickness  on  the  outer  sur- 
faces and  tied  and  bonded,  but  the  extreme  outer  edge  of  the  flanges  of 
beams,  or  plates,  or  angles  connected  to  the  beams,  may  project  to  within 
2  ins.  of  the  outside  surfaces  of  the  brick  casing. 

"The  inside  surface  of  girders  may  be  similarly  covered  with  brick- 
work, or  if  projecting  inside  of  the  wall,  they  shall  be  protected  by  terra 
cotta,  concrete  or  other  fireproof  material." 


Diagram  No*  40. 

For  giving  the  thickness  and  weight  of  walls  for  skeleton  struc- 
tures, warehouses  or  dwelling  houses  according  to  the  New  York 
Building  Code. 


(132) 


GERMAN,    BELGIAN  AND   ENGLISH  I-BEAMS.  133 


CHAPTER  XIII.     GERMAN,  BELGIAN  AND  ENGLISH 

I-BEAMS. 

It  may  be  of  interest  to  the  designer  to  compare  foreign  prac- 
tice in  rolled  beams  with  American  practice.  For  this  reason  Tables 
Nos.  32,  33  and  34,  have  been  prepared,  giving  the  principal  dimen- 
sions of  I-beams  made  in  Germany,  Belgium  and  England  respec- 
tively. 

GERMAN  I-BEAMS :— This  list  of  shapes  is  a  most  interesting 
series  from  a  theoretical  point  of  view.  The  increments  of  increase 
of  weight,  thickness  of  web  and  strength  follow  almost  a  perfect  law 
of  symmetry.  From  a  practical  aspect  there  is  little  of  value  in  them 
that  would  appeal  to  the  American  mind ;  there  are  27  different 
heights  between  5^  ins.  and  2 if  ins.,  inclusive,  while  the  ten  dif- 
ferent heights  adopted  by  the  American  Association  of  Steel  Manu- 
facturers in  1896  for  beams  6  ins.  and  over  already  seem  too  many. 

In  this  table  the  section-moments  are  given  on  a  basis  of  8 
tons  per  sq.  in.  allowable  fiber  stress.  These  are  given  more  for 
comparative  than  for  practical  value.  In  fact,  if  this  table  is  used 
for  designing  beams,  it  would  be  advisable  to  use  only  70%  of  the 
section-moment  given,  unless  the  material  passes  the  American 
standard  inspection. 

BELGIAN  I-BEAMS: — Representative  Belgian  I-beams  are 
listed  in  Table  No.  33.  These  shapes  are  somewhat  nearer  the  sec- 
tions adopted  in  this  country;  there  being  from  two  to  four  dif- 
ferent beams  rolled  for  each  height.  Otherwise,  what  has  been  said 
as  to  strength  and  adaptability  of  German  shapes  to  American 
needs,  applies  to  the  beams  of  this  group. 

ENGLISH  I-BEAMS :— Table  No.  34  shows  a  series  of  English 
sections  of  I-beam.  As  might  be  expected,  these  shapes  conform 
much  more  to  the  American  system  of  rolling  I-beams  than  any 
other.  The  values  for  the  section  moments  are  given  on  a  basis 
of  8  tons  per  sq.  in.  allowable  fiber  stress. 


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136  STRUCTURAL    DESIGNERS'    HANDBOOK. 


CHAPTER  XIV.     FLEXURAL  EFFICIENCY  OF  I-BEAMS 
AND  CHANNELS. 

An  interesting  matter  in  connection  with  the  design  of  beams 
and  girders  is  the  relative  "efficiency"  of  the  different  standard  sec- 
tions. An  8-in.  18  Ibs.  I-beam  has  a  certain  section  moment.  If 
this  beam  be  taken  as  a  standard  of  comparison,  then  the  value  of 
its  section-moment  divided  by  18  may  be  taken  as  a  unit  of  effi- 
ciency, i.  e.,  1 00%.  Thus  a  2O-in.  65  Ib.  I-beam,  for  instance,  shows 
a  much  greater  bending  strength  per  pound  of  metal  contained  in 
a  lineal  foot  of  the  beam , 

DIAGRAM  NO.  41  herewith  gives  curves  representing  the  rel- 
ative efficiency  of  all  the  standard  and  special  section  of  I-beams 
and  channels.  In  this  diagram  abscissas  represent  efficiencies, 
based  on  the  above  standard.  Ordinates  represent  weights  per 
lineal  foot.  Different  lines  drawn  on  the  diagram  represent  the 
various  sections  of  beams.  The  full  heavy  lines  represent  the 
I-beams  of  the  American  Association  of  Steel  Manufacturers.  The 
light  full  lines  represent  Pencoyd  I-beams  (only  shown  where  they 
differ  considerably  from*  the  Association  standards).  The  dotted 
lines  represent  standard  and  special  channels. 

As  a  matter  of  comparison  some  foreign  sections  of  I-beams 
are  also  represented  on  this  diagram.  The  solid  dots  represent 
some  of  the  oddest  of  the  Belgian  I-beams.  The  depth  of  the 
beam  is  in  each  case  noted  next  the  dot  in  figures  representing 
inches.  In  like  manner,  a  number  of  representative  German  sec- 
tions of  I-beams  are  shown  by  circles  with  black  centers.  The  sizes 
they  represent  are  given  as  for  the  Belgian  shapes. 


FLEX  URAL  EFFICIENCY  OF  I-BEAMS  AND  CHANNELS.       137 

Diagram  No*  4f 

For  giving  the  relative  flexure  efficiency  of  I-beams  and  chan- 
nels per  pound  of  steel. 


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138  STRUCTURAL    DESIGNERS'    HANDBOOK. 


CHAPTER  XV.    BASES  AND  LINTELS  OF  CAST  IRON. 

CAST  IKON  BASES  OR  SHOES  FOR  COLUMNS:— These  usu- 
ally bear  upon  concrete,  dimension  stone,  brickwork  or  upon  grill- 
age footings.  They  are  usually  set  in  place  upon  small  blocks  and 
grouted  with  Portland  cement  paste  from  one-half  to  three-fourths 
of  an  inch  in  thickness.  A  better  practice  is  to  ram  the  Portland 
cement  mortar  in  from  the  side  of  the  shoe,  to  do  which  requires 
not  less  than  an  inch  and  a  half  to  two  inches  of  clear  space  under 
the  shoe  when  temporarily  supported  by  the  blocks. 

The  area  of  the  bottom  side  of  this  shoe  is  determined  by  the 
allowable  unit  pressure  on  the  supporting  material.  The  height 
and  thickness  of  metal  depend  upon  a  variety  of  certain  and  uncer- 
tain conditions.  Only  a  few  of  the  more  important  of  these  con- 
ditions will  be  considered  because  they  arise  in  specific  cases  rather 
than  in  general  practice. 

A  slight  unevenness  in  the  grouting  of  a  cast  iron  shoe  is  not 
an  unusual  occurrence,  and  this  is  sure  to  set  up  irregular  and 
indeterminate  stresses  in  the  metal.  When  grillage  beams  are 
used  in  footings  the  slightest  deflection  of  the  beams  will  cause  the 
load  on  the  shoe  to  be  carried  on  its  two  edges  at  right  angles  to 
the  beams.  The  distance  of  the  webs  or  ribs  apart  should  never 
exceed  the  limits  fixed  by  the  strength  of  the  bottom  plate  between 
these  webs. 

A  "rule  of  thumb"  method  of  designing  cast-iron  shoes  is  to  let 
h   ==   iM   a  (25) 

where  h  =  height  of  shoe, 

a  =  projection  of  shoe  beyond  the  edge  of  the  column. 
The  thickness  of  metal  is  made  the  same  as  that  of  the  column  sup- 
ported. 

The  purely  theoretical  methods  for  computing  the  flexure 
strength  of  shoes  are  laborious  and  tedious.  The  following  sim- 
ple empirical  formulas  give  results  within  a  very  small  percentage 
of  absolute  accuracy.  Two  cases  are  considered : 

(1)  When  a  uniform  unit  pressure  is  assured  on  the  bottom  of 
the  shoe — for  instance,  a  bearing  on  a  granite  block. 

(2)  When  the  load  is  likely  to  be  carried  on  two  edges  "of  the 
shoe — a  condition  existing  when  grillage  footings  are  used. 


BASES   AND   LINTELS    OF   CAST   IRON.  139 

FIRST  CASE:— 

a2  W 

A (26) 

(2  a  +  b)        h 
where  a  =  projection  in  inches. 

b  =»  diameter  of  column  in  inches, 
h  =  height  of  shoe  in  inches. 
W  =  total    load    in   tons. 

A  =  area*  of  cross  section  (in  square  inches). 
SECOND  CASE:— 

A  -  —  W  (27) 

h 
where  the  values  are  same  as  above. 

When  the  thickness  of  metal  in  the  various  parts  of  a  cast  iron 
shoe  is  not  uniform,  or  nearly  so,  flaws  are  apt  to  develop  in  the 
process  of  the  cooling  off  of  the  casting.  For  this  reason  the  de- 
sign of  an  economical  shoe  requires  skill  in  choosing  the  height  and 
distance  apart  of  the  webs  so  that  the  metal  in  the  several  parts 
shall  be  one  thickness.  The  thickness  of  metal  directly  under  the 
column  section  must  always  be  sufficient  for  the  load  on  the 
column. 

The  safe  limits  for  the  distance  between  the  webs  or  ribs  of 
cast  iron  shoes  are  given  on  DIAGRAM  NO.  42  herewith.  It  gives 
the  safe  distance  in  inches  for  various  unit  loads  on  the  bottom  of 
the  shoe  and  for  various  thicknesses  of  metal  in  the  bottom  plate. 
EXAMPLE: — For  a  unit  pressure,  on  the  bottom  of  a  shoe  of  nl/2 
tons  per  sq.  ft.,  the  brackets  should  not  be  more  than  10  ins.  apart  for  i^-in. 
metal  in  the  bottom  plate,  while  for  18  tons  the  metal  should  be  2  ins.  for 
the  same  spacing  of  brackets. 

CAST  IRON  LINTELS:— When  the  height  of  the  stem  of  a  cast 
iron  lintel  is  not  less  than  about  4/10ths  of  the  width  of  the  lintel 
per  stem,  the  formulas  following  can  safely  be  used.  Two  stems 
should  be  used  for  widths  greater  than  16  ins. 

B  L3      Wab 
A  =  —     -  +  -      — ,  (28) 

115  h      83  L  h 

where  A  —  area  of  cross  section  of  lintel  at  the  centre  in  square  inches. 
B  =  thickness  of  brick  wall  in  inches. 
L  =  span  of  lintel  in  feet. 

h  —  height  of  cross  section  at  centre  of  lintel  in  inches. 
W  =  concentrated  load  (at  distance  a  and  b  from  each  end)  in  Ibs. 
(Note: — If  more  than  one  concentrated  load  occurs  W  a    b 
=  W  a'  b'  +  W"  a"  b"  +  etc. 

*This  area  includes  only  the  area  of  the  ribs  at  a  distance  "a"  from  the 
«dge  of  the  shoe  plus  the  area  of  the  base  plate. 


140 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


Diagram  No*  42 

For  giving  the  minimum  thickness  for  bottom     plate  of  cast- 
iron  shoes. 

CLEAR  DISTANCE  BETWEEN  BRACKETS 


10" 


15"  20" 


3 


.Xu 


•Jfc 


2" 


/ 


<-y 


/ 


10" 


15" 


20" 


CLEAR  DISTANCE  BETWEEN  BRACKETS 


3ASES  AND   LINTELS   OF  CAST  IRON.  141 

The  width  required  for  a  lintel  is  always  known  and  in  the 
case  of  brick  walls  is  usually  8,  12,  16,  20,  24  or  28  ins.,  according 
to  the  thickness  of  the  wall  above  it ;  with  the  above  formula,  by 
assuming  a  height  for  the  lintel,  say  6,  8,  10  or  12  ins.,  and  deciding 
upon  the  use  of  one  or  two  sterns,  the  area  of  the  cross  section  is 
found  from  the  first  factor  of  the  above  formula  if  no  concentrated 
load  occurs;  and  from  the  summation  of  the  factors  when  one  or 
more  concentrated  loads  occur  along  with  the  brick  wall  load. 


142  STRUCTURAL    DESIGNERS    HANDBOOK. 

CHAPTER  XVI.     WOODEN  BEAMS  AND  POSTS. 

For  structural  purposes  wood  is  almost  exclusively  employed 
in  rectangular  form.  This  uniformity  of  section  makes  the  appli- 
cation of  wood  to  framing  a  comparatively  simple  problem;  and 
lends  itself  peculiarly  to  independent  diagram  treatment  for  the 
solution  of  such  problems.  This  will  be  evident  from  the  descrip- 
tion of  the  diagrams  presented  in  this  chapter  without  further  dis- 
cussion on  the  mechanics  of  the  subject,  the  treatment  of  which 
has  been  fully  covered  in  Part  I. 

SAFE  LOADS  ON  WOODEN  JOISTS. 

Two  sets  of  diagrams  are  given,  one  set  (Diagrams  Nos.  43 
and  44)  for  the  strength  of  white  pine,  spruce  or  chestnut  joists, 
for  various  depths  from  3  to  16  ins. ;  the  other  set  (Diagrams  Nos. 
45  and  46)  for  yellow  pine  and  locust. 

DIAGRAMS  FOR  WOODEN  JOISTS:— In  each  diagram  ab- 
scissas represent  span  of  joist  in  feet;  the  ordinates  represent  spac- 
ing of  joists  in  inches ;  curves  on  the  diagrams  show  safe  load*  in 
pounds  per  square  foot  of  floor.  The  spans  represented  vary  from 
3  to  30  ft.,  and  the  spacings  from  12  to  24  ins.,  and  the  load  per 
square  foot  from  I  to  1,000  Ibs. 

The  load  lines  show  a  bend  which  indicates  where  deflection 
enters  as  a  factor.  For  spans  to  the  right  of  the  bend  the  beams 
are  designed  for  a  limiting  deflection  of  one  four-hundredth  of  the 
span. 

NOTE: — If  oak  joists  are  to  be  used,  work  out  the  problem  by  each  of 
the  preceding  sets  of  diagrams,  and  take  a  mean  of  the  two  results. 

It  will  be  evident  that  floor  planking  3  ins.  or  over  in  thickness 
can  also  be  figured  by  these  diagrams. 

SAFE  LOADS  ON  WOODEN  GIRDERS. 

Two  sets  of  diagrams  (including  Nos.  47  to  50)  are  also  given 
for  these  as  in  the  preceding. 

DIAGRAMS  FOR  WOODEN  GIRDERS :— These  diagrams  are 
constructed  the  same  as  those  for  joists.  The  depths  of  girders 
represented  by  the  diagrams  run  from  6  to  16  ins. ;  spans  from  3 

*It  is  to  be  remembered  that  the  diagrams  are  for  beams  I  in.  wide; 
for  a  beam  2  ins.  wide  double  the  load  obtained  from  the  diagram;  for  a 
beam  3  ins.  wide,  triple  the  load.  etc. 


WOODEN    BEAMS    AND     POSTS.  143 

to  25  ft.  are  shown,  and  loads  from  I  to  100  Ibs.  per  sq.  ft.  The 
spacing  of  girders  represented  by  the  ordinates  is  given  in  feet 
and  runs  from  7  to  18  ft.  The  limiting  deflection  is  same  as  in  the 
preceding  diagrams.  The  diagrams  are  also  for  girders  I  in.  wide. 

SAFE  LOADS  ON  V'OODEN  POSTS. 

The  strength  of  wooden  posts  is  represented  on  Diagram  No. 
51.  The  general  arrangement  of  this  diagram  is  similar  to  those 
for  steel  and  cast  iron  columns.  It  is  constructed  on  the  basis  of 
the  stresses  provided  by  the  "Code"  (N.  Y.  C.)  and  is  a  combina- 
tion of  three  distinct  diagrams  representing,  respectively,  white  :  -.1 
pine,  white  oak,  and  yellow  pine.  In  all  three  diagrams  abscissas 
represent  column  ratios,  ordinates  represent  area  of  section,  and 
the  curves  represent  concentric  loads. 

It  will  be  noted  that  the  upper  scale  of  abscissas  differs  from 
the  scale  at  the  bottom  of  the  diagram.  The  former  represents  the 
ratio  of  slenderness  of  the  posts  as  hitherto  defined — the  quotient 
of  the  length  divided  by  the  radius  of  gyration  of  the  cross  section 
— and  is  given  so  that  Diagrams  Nos.  30,  32  and  34  can  be  com- 
bined with  it  for  the  purpose  of  designing  wooden  posts  for 
eccentric  loads.  The  latter,  the  scale  at  the  bottom,  represents  ,  , 

another  ratio  much  used  for  wooden  posts :  the  length  divided  by 
the  least  width  of  the  section.  This  latter  ratio  is  the  one  com- 
monly used. 

Two  supplementary  ordinate  scales  are  given  at  the  right  of 
the  diagram.  The  first  of  these  shows  the  usual  sizes  of  posts,  at 
proper  vertical  intervals  to  represent  the  areas  given  on  the  ordi- 
nate scale  on  the  extreme  left.  One  column  is  given  for  square 
posts,  another  for  round  posts. 

The  other  supplementary  scales  show  the  weight  per  lineal 
foot  for  any  cross  section  area  of  post.  One  column  is  given  for 
white  pine  and  another  for  yellow  pine  and  white  oak  which  woods 
are  approximately  twice  as  heavy  as  white  pine. 

EXAMPLE: — Posts  of  white  pine,  white  oak  or  yellow  pine  10"  x  10" 
will  carry  concentric  loads  of  32  to  18  tons,  36  to  20  tons,  or  40  to  23  tons, 
respectively,  for  unsupported  lengths  of  25  ft.  to  8  ft.  4  ins. 


144 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


Diagram  No*  43 

For  giving  the  safe  load  on  white  pine,  spruce  or  chestnut 
joists  for  each  inch  in  breadth. 

PERTH    OF   JO\5J5      3" 


\ 


9    10 


15  20  „, 

PERTH  Or   JOISTS       4 


o 
d   - 


PERTH  OF  j0is>Tb    6"  ^  £ 


2   "  \\\\\\\  V\\  \  \  \X\W\N\\\W  \\  \  N\\\  \  \  ^     \      N 


8      9     JO 

SPAN  OF  JOISTS  IN  FEET 


3O 


WOODEN  BEAMS  AND   POSTS.  145 

Diagram  No*  44 

For  giving  the  safe  load  on  white  pine,  spruce  or  chestnut 


joists  for  each  inch  in  breadth. 


PERTH  Of  JO\5Tf> 


10 


vo 


. 


\\ 


\ 


\\\ 


\\ 


1  \ 


fc 

a 


&       9      10 


PERTH 


I21 


\    3 


_ 

\ 

~ 


15  20 

DEPTH    OF  JO»5T      16 


\\ 


\\\ 


\\\\ 


\ 


\\\ 


^1 


\\ 


6        7       &     9     10 

SPAN  OF  JOISTS  IN  FEET 


20 


25       30 


146 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


Diagram  No*  45 

For  giving  the  safe  load  on  long  leaf  yellow  pine  or  locust 
joists  for  each  inch  in  breadth. 


DEPTH  OP  J01575        4" 


15  20 

D&PTH     OP  J£»£T£ 


OP    JOI5T5 


»    O 


V0 


Nk\\ 


\\\ 


\\ 


\\ 


\\ 


\\ 


\\ 


\\\\ 


\\\> 


7       &      9     \O  .15 

SPAN  OF  JOISTS  IN  FEET 


20 


3O 


WOODEN  BEAMS 


Diagram  No*  46 

For  giving  the  safe  load  on  long  leaf  yellow  pine  or  locust 
joists  for  each  inch  in  breadth. 

DEPTH    OF 


15  ZO  3O 

PERTH   OF    JOISTS  =  14" 


7        8      9     IO  15 

SPAN  OF  JOISTS  IN  FEET 


20 


25         30 


148 


STRUCTURAL    DESIGNERS1    HANDBOOK. 


Diagram  No.  47 

For  giving  the  safe  load  on  white  pine,  spruce  or  chestnut 
girders  for  each  inch  in  breadth. 

PERTH   Of  WRITER        6" 


\\\\\\\\  \\  \  \  \ 


\v 


xw 


XXXxNXX 


\A\\  \  \   \ 


\ 


\ 


\ 


\  \ 


\kx 


\$ 


\5 


CO 


If 


a    s  10 


PePTh  OF   GIRPER      8" 


\\\\\\\\ 


\\ 


\v\\v\\ 


\\ 


\\\ 


\ 


7      &     9     \0  \5 

SPAN  OF  GIRDER  IN  FEET 


20          7.5 


WOODEN  BEAMS  AND   POSTS. 


149 


Diagram  No*  48 

For  giving  the  safe  load  on  white  pine,  spruce  or  chestnut 
girders  for  each  inch  in  breadth. 

PEPTH    OP    GIRPE-R      12" 


~  VvV  \\V\\\\\VA\VA 


10  15  20  in 

PfPTH   OP    GIRPrrR    14 


\\\V\\\  v\\\\\\\\\A\\\\\\\\U\\  v\>  \  \  \    \ 


\ 


\\\\v 


x\\v\ 


\\ 


\A\ 


\\ 


\\\\ 


678 


10 


15  20 

PEPTH     OP   GIRPER 


16' 


\\\\  .\\\ 


\ 


ss 


\\ 


\\\v 


\\ 


\\ 


\\\\ 


^ 


\\\ 


VN 


\c\ 


\\\ 


\\\ 


SSSwSss^SSSSvS^sv 


\  \   \ 


\\vv 


^\\ 


\\ 


v\\ 


sis:: 


\ 


O 


c? 


e        7       8      9     \Q  15 

SPAN  OF  GIRDER  IN  FEET 


2O 


25 


^ 
30 


ISO 


STRUCTURAL    DESIGNERS'    HANDBOOK. 


Diagram  No.  49 

For  giving  the  safe  load  on  long  leaf  yellow  pine  or  locust 
girders  for  each  inch  in  breadth. 

PERTH   OF    (TlffPER       6" 


Ift 


\\\ 


WOs 


SSSS 


\\\ 


\\ 


\\\ 


\\\\ 


\\ 


\ 


ss 


\\ 


\\ 


\ 


S^SMSS^ 


\\\\\\  v  IM  irm 


\\ 


\A 


\N^ 


A? 


\k 


u 


UJ 

UJ 

**•  <a 


&     9 


en   — 


o 
z 

o 

£ 


3 


Q 


15  20  30 

DEPTH    ^?F    CIRDeR     8" 


o 


S     9    to 

OF  GIRDER  IN  FE 


2&       30 


ET 


WOODEN   BEAMS  AND   POSTS. 


Diagram  No.  50 

For  giving  the  safe  load  on  long  leaf  yellow  pine  or  locust 
girders  for  each  inch  in  breadth. 

PEPTH     Or   GIRC7ER     12* 


15  2O 

P&PTH   OP  GIRDER     14 


\\\ 


\  \ 


\\ 


\N\\\ 


\\ 


\v 


\\\ 


\v 


\\ 


\\ 


\\\x\ 


\\\\ 


\\\ 


\\\ 


\\\\ 


\\ 


Ift 


B      9     IO 


15  20 

PERTH     OF   GIRPE-R 


\\\\\ 


NvV\ 
VX 


\ 


\\ 


\ 


\A 


^ 


s 


^ 


S3 


N^X 


\\ 


>v 


N^ 


\\\ 


\ 


\\ 


S 


\\ 


\\ 


\\ 


\' 


V 


\ 


5S 


i^^^^N\s\\\ 


-7    a 

SPAN  OF 


3     10  15 

GIRDER  IN  FEET 


\\ 


20 


25       30 


152  STRUCTURAL    DESIGNERS1    HANDBOOK. 

Diagram  No.  5J 

For  giving  the  safe  load  on  wooden  posts. 


AREA  OF  SECTION  IN   SQUARE  INCHES 


INDEX. 

Page 

American  Assoc.  of  Steel  Mfrs. : 

Standard  shapes  14 

Angles : 

Radius  of  gyration 102—106 

Section    area .102—106 

Section  moment   102,  106 

Steel: 

Table  for  beams,  girders,  columns,  or  truss  members 

having  even  and  uneven  legs 102 — 106 

Thickness  of  metal   102—106 

(See  also  Connection  Angles.) 

Angles  and  Tees: 

Explanation  of  diagrams  for 14 

Base 63 

Bases,  cast  iron: 

For   columns    138,  140 

Beams: 

Angles,  diagrams  described   14 

Belgian  I 133—135 

Buckling  of  compression  flange 4 

Cross  section 1 

Definition   of    11 

Deflection 2 

Diagram,  concentrated  load  converted  to  uniform  load..      52 
Diagram,  concentrated  load  at  any  point  reduced  to  con- 
centrated load  at  middle   56 

Diagram  for  I-beams,  3-in.  to  24-in 19 — 47 

Diagrams  for  angles  and  tees,  spacing  and  span  for  given 

loading    48—51 

Diagram  for  grillage  beams 63 

Diagram,   deflection   various   loadings   on   3-in.    to   15-in. 

I-beams 57 

Diagram,  deflection  various  loadings'  on  10-in.   to  24-in. 

I-beams 58 

Diagram  for   converting  concentrated  load  to  equivalent 

uniform    load 15 

Diagram,  safe  loads  on  3-in.  to  15-in.  channels 591 

Diagram,  spandrel  beams 56 

Diagrams,  utility  of 11 

English  I   133—135 

End  reactions $ 

Explanation  of  diagrams    12 

Explanation  of  diagrams  for  I-beams  and  channels  ....     54 

Explanation  of  tables 13,     14 

Flexural  efficiency,  I-Beams 136,  137 

German  I 133 — 135 


154  INDEX. 

Page 
Grillage.     (See  Grillage  Beams.) 

Loads % 4 

Manner   of   support    2 

•Maximum  end  reaction   13 

Maximum  per  cent,  of  bending  load 13 

•Mechanics  of 1 

Method  of  using  diagram  for  I-beams   12 

Properties  of 85 

Properties  of   Foreign    134,  135 

Resistance 1 

'Section    moment    1 

Span    1 

Spandrel 53,  54 

Steel,  I — Tables  for  beams,  girders,  columns  or  truss  mem- 
bers  90-93 

Tables  for    3-in.  I-beams,  channels  and  zees IS 

,               4-in.   I-beams,  channels  and  zees -0 

5-in.  I-beams,  channels,  zees  and  bulb  angles '22 

6-in.  I-beams,  channels',  zees  and  deck  beams 24 

7-in.  I-beams,  channels,  zees  and  bulb  angles 26 

8-in.  I-beams,  channels,  deck  beams  and  angles.  ...  28 

9-in.  I-beams,  channels,  deck  beams  and  angles.  ...  30 

10-in.  I-beams,  channels,  deck  beams  and  angles.  ...  32 

12-in.  I-beams,  channels  and  deck  beams 34 

12-in.  I-beams  and  channels 3(1 

15-in.  I-beams  and  channels  38,  3!) 

18-in.   I-beams    42 

20-in.  I-beams   44 

24-in.   I-beams    46 

Tees,  explanation  of  diagrams  14 

Unit  stress  2 

Beam  work H 

Bearing  capacity  of  soil 128 

Bearing  plates: 

Design  of   67 

Tables  of 7O-71 

Brick  walls.     (See  Walls,  Brick.) 

Brickwork,  safe  load  on .     68 

Buckling  of  compression  flange    4 

Buckling  of  web   62,     64 

Cast  iron  bases  and  lintels 138 

Channels— 'Beams.     (See  Beams.) 

Channels: 

Flexural    efficiency    136,  137 

Height  of    94,     96 

Section  area 94—96 

Tables  for  beams,  girders,  columns,  truss'  members.  ...94 — 97 

Web  thickness 94—96 

Weight    per    foot    94—101 

Channel  columns.     (See  Columns,  Plate  and  Channel.) 

Columns: 

Base,   cast  iron  or  steel 60 

Built  steel  shapes ,    88 


INDEX.  155 

Page 

Columns.     Continued. 
Cast  Iron, 

Design  of 112 

Diagrams  giving   safe   loads'    as    recommended    by    the 

author 115 

Diagrams   giving  safe  loads   as   specified   by   New  York 

Building  Code 114 

Diagram  giving  weight  in  pounds  per  foot,  thickness  of 

metal  and  outside  diameter 116 — 118 

Channel   88 

Concentric  loads 8 

Cross  section  of 9 

Diagram  for  eccentric  loading 83 

Diagram   giving  radius  of  gyration  of  the   most  common 

forms  of  built-up  sections 80 

Diagram  giving  radius  of  gyration  of  the   most   common 

forms  of  wood,  cast  iron  or  steel  sections 79 

-  Diagram  giving  ratio  of  slenderness 81 

Diagram  giving  safe  loads,  New  York  Building  Code,  for 
ratios  of  slenderness  up   to   120  and  as   recommended 

by  the  author  for  ratios  120  and  200 82 

Eccentric  loads 8 

Footings 60 

Mechanics  of   1 

Plate  and  angle 89 

Radius  of  gyration 72 

Ratios'  of  slenderness   73 

Designing  built  columns 72 

Table  for  plate  and  angle   107 

Tables  for  plate  and  channel 98—101 

Weights  of 98—101 

Zee-bar    89 

Columns  and  truss  members 72 

Connection  angles: 

Bearing    values     69 

Design  of 60 

End  reaction    67,     69 

Holes  in  shop  or  field  end 69 

Rivets 70 

Shearing  values    69 

Diagram,  explanation  of  equivalent  load  on  spandrel  beams..     53 
Diagrams.     (See  Beams,  Diagrams;  Columns,  Diagrams,  etc.) 

Dimensions  and  weights    85 

Dimensions  for  practical  detailing 91 — 110 

End  reaction,  allowable.     (See  Beam  Tables.) 

End  reactions 3,  13,  14,  65,  67,  69,  70,  91,     93 

Beams: 

Connection  angles   67,     69 

Explanation  of  diagram  65 

Floor: 

Explanation  of  diagram  for  converting  concentrated  load 

to  equivalent  uniform  load 15 

Diagram  for  converting  concentrated  load  to  uniform  load.   52 


156  INDEX. 

Page 
Floor  arches: 

Weight  of   123 

Floor  beams,  wooden: 

Weight  of 123 

Floor  framing 11 

Diagram  giving  weight  of  steel  where  loads  are  a  mini- 
mum     120 

Diagram  giving  weight  of  steel  where. loads  are  a  maxi- 
mum    121 

Floor  framing,  steel: 

Weight  of    119 

Floor  Girders: 

Conventional  method  of  treating  load  on   5 

Flooring  material: 

Weight  of    123 

Footings   60 

Diagram  for  grillage  beams    63 

Live  load  on   1^5 

Foundation  walls  131 

Girders.     (See  Beams,  Definition  of;   Plate  Girders.) 

Grillage    beams    60 

Conventional  methods  of  considering  loads  on   7 

Explanation    of   diagram 62 

Diagram,  safe  pressure  in  tons  per  sq.  ft 63 

Illustration  of  footing 61 

Load  on   5 

I-Beams.     (See  Beams.) 

Joists,  weight  per  sq.  ft.  of  floor 122 

(See  also  Beams'.) 

Lattice    bars \ 84,  95,  97 

Lintels,    cast-iron    139 

Load,  allowable  per  sq.  ft.     (See  Beam  Tables.) 

Loads,  dead: 

Carried  by  columns   119 

Carried  by  floor  girder 119 

Loads: 

Diagram  for  eccentric  column  loading 83 

Explanation  of  diagram   for  reducing  concentrated   load 

to  equivalent  uniform  load   16 

Explanation  of  equivalent  load  diagram 53 

Loads,  live,  New  York  Building  Code    124,  125 

On    beams    4,    57,     58 

On  columns 8 

On  floor  girders   5 

On  footing 125 

On  grillage  beams   5,       7 

On  wooden  girders    143,   148—151 

On  wooden  joists    142,  144—147 

On    wooden   posts    .  . . . 148,  152 

Web  in  compression  91 — 93 


INDEX.  157 

Page 

Partitions  ; 

Weight  of 124 

Plate  and  angle  columns.     (See  Columns,  Plate  and  Angle.) 

Plate  girders: 

Design    of    87 

Properties   of    86 

Plates,  'bearing.     (See  Bearing  Plates.) 

Plates,  thickness  of   98—101" 

Pressure,   wind    125 

Properties  of  Foreign  I-beams 134,   135 

Radius  of  gyration 72,  79,  80,  83,  91,  98,  102—106,  108—110 

Diagram  common  forms',  wood,  cast-iron  or  steel  sections.     79 
Diagram  built  up  sections  80 

Rafters.     (See  Beams.) 

Reactions.     (See  End  Reactions.) 

Retaining  walls,  thickness  of   131 

Rivets: 

Diameter  of 91—97 

Gage  of  lines 91—97 

Relative  values  various  sizes 69 

Size  of 102—103 

Size  and  gage  for  zee-bars j. 110 

Rubble,  safe  load  on 68 

Section  areas: 

For  concentric  loading   75 

For  concentrically  loaded  columns  with  pin  ends 76 

For    eccentric    loading    77 

For   tension   members    76 

Section  moment 1,  91—97,  101—106,  108,  109 

Shapes.     (See  Structural  Shapes.) 

Soil,   bearing   capacity    128 

Spacing  c.  to  c.     (See  Beam  Tables.) 

Span,  allowable.     (See  Beam  Tables'.) 

Spandrel  beams,  explanation  of  diagrams 53 

Standard  shapes   14 

Steel,  flat  rolled,   weight  of   Ill 

Steel  angles.      (See  Angles  Steel.) 

Steel  columns.     (See  Columns.) 

Strength  of  web   91—93 

Stresses,  unit: 

Safe  load  on  masonry  work 126 

Strength   of   columns    126 

Working  stresses: 

Compression    (direct)     127 

Safe  extreme  fiber  stress   (bending)    128 

Shear    128 

Tension   (direct)    128 

Structural  shapes,  properties  of 16,     84 

Table's.      (See   Beams,   Columns,   Connection  Angles,   etc.) 


158  INDEX. 

Page 
Tees: 

Beam  diagrams  described    14 

Dimension   and    weights'    108,  101) 

Radius  of  gyration    108,  109 

Section  moment   108,  109 

Tables  for  beams,  girders,  columns  or  truss  members.  108,   109 

Template,  size  of   70 

Timber.      (See  Wood.) 
Trusses: 

Design    of    , 86 

Properties  of   86 

Unit  stresses.     (See  Stresses,  Unit.) 
Walls: 

Footing 60 

Foundation    131 

Retaining,   thickness  of   131 

Thickness  and   weight 129,  132 

Walls,  brick: 

Weight  of    124 

For  dwelling  houses 129 

For  inclosing  skeleton   structures    129,  131 

For  warehouses   129 

Web: 

Buckling    of    62,  64 

Compression  allowable  load 91—93 

Strength  of    - 91—93 

Thickness 94,  96 

(See  also  Beam  Table.) 

Weight,  floor  framing.     (See  Floor  Framing.) 
Weight,  per  foot.     (See  Beam  Tables.) 

Weight,  flat  rolled  steel Ill 

Weights  and  dimensions  per  lineal  foot 85 

Wind   pressure    125 

Wooden  girders,  safe  loads 143,  148—150 

Wooden  joists,  safe  loads  142,  144—147 

Wooden  posts,   safe   loads    143,  152 

Zee-bars    89,  110 

Flange  width   110 

For  beams,  girders,  columns  or  truss  members 110 

Radius  of  gyration 1 10 

Size  and  gage  of  rivets   110 

Thickness  of  metal    110 

Web  height 110 

Weight   per  foot 110 

Width  of  web  plate .   110 


V     i  O  I 


